Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value ...Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.展开更多
This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four...This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.展开更多
In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′...The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.展开更多
HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.T...HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.This study investigates the competitive biochemical interplay between reverse transcriptase(RT)and integrase(IN)enzymes,employing a fractional calculus framework to model their mutual inhibitory effects.Through the application of fixed-point theory and Picard stability analysis,the existence,uniqueness,and stability of the fractional-order system are rigorously established.The role of RT-IN enzymatic competition in influencing HIV replication dynamics is elucidated through global sensitivity analysis using Latin Hypercube Sampling.Furthermore,the model incorporates memory-dependent characteristics by examining three distinct fractional operators,namely,the Caputo,Caputo-Fabrizio,and Atangana-Baleanu operators in the Caputo sense,thereby elucidating their respective influences on system behavior.The Atangana-Baleanu operator,in particular,demonstrates an enhanced capacity to capture the complex,synergistic processes underpinning HIV progression.This research provides a critical nexus between molecular virology and applied mathematics,offering foundational insights for the advancement of more precise and targeted therapeutic strategies against HIV.展开更多
Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral ...Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral techniques have achieved many exciting results in soil metal monitoring due to their advantages of being fast and non-destructive.However,insufficient attention has been paid to lithium in soil,and the feasibility of its estimation using hyperspectral techniques needs to be investigated.We studied 97 soil samples from claytype lithium mines in the Ertanggou area of the East Tianshan Mountains of Xinjiang to explore the effects of spectral resolution,fractional order derivatives(FOD),and characteristic band selection on the estimation accuracy of clay Li content,to obtain a fast and effective method for estimating clay Li content.Finally,we developed a new method for rapid and nondestructive estimation of soil lithium content.We have obtained some important results from the study.Spectral resolution exerts a significant impact on model performance,and its reduction usually leads to a decline in model performance.For the full band,the models constructed with low-order derivatives were superior to those with high-order derivatives,and the best model was obtained at the 0.4-order derivative(coefficient of determination(R^(2))and relative predictive deviation(RPD)of 0.777 and 2.118,respectively).In the characteristic bands,the lower order is sensitive to the visible-near-infrared range,and the higher order is sensitive to the short-wave infrared range,and the model constructed with the higher-order derivatives outperforms the lower-order derivatives.In this study,the combination of FOD and Random Forest(RF)can significantly improve the model performance,with R^(2),Relative Root Mean Squared Error(RRMSE),and RPD being 0.849,1.526,and 2.574,respectively.Therefore,this research provides a theoretical basis and technical reference for imaging hyperspectral exploration of anomalous areas of clay-type Li resources.展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Num...The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Numerical simulations,such as exact diagonalization,density matrix renormalization groups,matrix product states,and Monte Carlo methods are essential for examining the properties of strongly correlated systems.Recently,density functional theory has been employed in this field within the framework of composite fermion theory.This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems,including ground state and low-energy excitations.Special attention is given to the insights provided by density functional theory regarding composite fermion behavior,edge effects,and the nature of fractional charge and magnetoroton excitations.The discussion critically examines both the advantages and limitations of these approaches,while highlighting the productive interplay between numerical simulations and theoretical models.Future directions are explored,particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.展开更多
Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the pr...Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.展开更多
In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,w...In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm.展开更多
In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizh...In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.展开更多
Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Nume...Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.展开更多
Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its u...Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.展开更多
This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreov...This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.展开更多
In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x...In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.展开更多
Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compar...Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compared to invasive FFR.To evaluate the performance of a DL-based CT-FFR technique,DeepVessel FFR(DVFFR).Methods This retrospective study was designed for iScheMia Assessment based on a Retrospective,single-center Trial of CTFFR(SMART).Patients suspected of stable coronary artery disease(CAD)and undergoing both CTA and invasive FFR examinations were consecutively selected from the Beijing Anzhen Hospital between January 1,2016 to December 30,2018.FFR obtained during invasive coronary angiography was used as the reference standard.DVFFR was calculated blindly using a DL-based CTFFR approach that utilized the complete tree structure of the coronary arteries.Results Three hundred and thirty nine patients(60.5±10.0 years and 209 men)and 414 vessels with direct invasive FFR were included in the analysis.At per-vessel level,sensitivity,specificity,accuracy,positive predictive value(PPV)and negative predictive value(NPV)of DVFFR were 94.7%,88.6%,90.8%,82.7%,and 96.7%,respectively.The area under the receiver operating characteristics curve(AUC)was 0.95 for DVFFR and 0.56 for CTA-based assessment with a significant difference(P<0.0001).At patient level,sensitivity,specificity,accuracy,PPV and NPV of DVFFR were 93.8%,88.0%,90.3%,83.0%,and 95.8%,respectively.The computation for DVFFR was fast with the average time of 22.5±1.9 s.Conclusions The results demonstrate that DVFFR was able to evaluate lesion hemodynamic significance accurately and effectively with improved diagnostic performance over CTA alone.Coronary artery disease(CAD)is a critical disease in which coronary artery luminal narrowing may result in myocardial ischemia.Early and effective assessment of myocardial ischemia is essential for optimal treatment planning so as to improve the quality of life and reduce medical costs.展开更多
Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numeric...Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.展开更多
In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω)...In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω),where s∈(0,1),Ω■G is a bounded open domain,(-△_(G))^(s)is the fractional sub-Laplacian,H_(0)^(s)(Ω)denotes the fractional Sobolev space,f(x,u)∈C(Ω×R),g(x,u)is a Carath′eodory function on Ω×R.Using perturbation methods and Morse index estimates in conjunction with fractional Dirichlet eigenvalue estimates,we establish the existence of multiple solutions to the problem.展开更多
A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating t...A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating the relative controllability of the Langevin delayed fractional system with multiple delays in control.For linear systems to be relatively controllable,necessary and sufficient circumstances are identified by introducing and employing the Gramian matrix.The sufficient conditions for the relative controllability of semilinear systems are ofered based on Schauder's fixed point theorem.As an unusual approach,the controllability results of the delayed system are built for the first time on the exact solution produced by the MittagLeffler type function although controllability ones in the literature are built on the Volterra integral equations or the mild solutions produced by resolvent families.展开更多
文摘Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2601).
文摘This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
基金Supported by Natural Science Foundation of China(12461021)。
文摘The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.
基金Supported by the DST FIST Programme(SR/FST/MS-II/2021/101(C))UGC-JRF(21161010788)+1 种基金supported by NSFC(11831003,12171111)SFC(KZ202110005011)。
文摘HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.This study investigates the competitive biochemical interplay between reverse transcriptase(RT)and integrase(IN)enzymes,employing a fractional calculus framework to model their mutual inhibitory effects.Through the application of fixed-point theory and Picard stability analysis,the existence,uniqueness,and stability of the fractional-order system are rigorously established.The role of RT-IN enzymatic competition in influencing HIV replication dynamics is elucidated through global sensitivity analysis using Latin Hypercube Sampling.Furthermore,the model incorporates memory-dependent characteristics by examining three distinct fractional operators,namely,the Caputo,Caputo-Fabrizio,and Atangana-Baleanu operators in the Caputo sense,thereby elucidating their respective influences on system behavior.The Atangana-Baleanu operator,in particular,demonstrates an enhanced capacity to capture the complex,synergistic processes underpinning HIV progression.This research provides a critical nexus between molecular virology and applied mathematics,offering foundational insights for the advancement of more precise and targeted therapeutic strategies against HIV.
基金Sponsored the National Natural Science Foundation of China(42502088)the National Major Science and Technology Project of China(2025ZD1007504-1)+2 种基金the Special Research Fund of Natural Science(Special Post)of Guizhou University(X202402)the Guizhou Provincial Science and Technology Projects(QKHJC[2024]youth 153)the Xinjiang Uygur Autonomous Region Natural Science Foundation(2024D01A147)。
文摘Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral techniques have achieved many exciting results in soil metal monitoring due to their advantages of being fast and non-destructive.However,insufficient attention has been paid to lithium in soil,and the feasibility of its estimation using hyperspectral techniques needs to be investigated.We studied 97 soil samples from claytype lithium mines in the Ertanggou area of the East Tianshan Mountains of Xinjiang to explore the effects of spectral resolution,fractional order derivatives(FOD),and characteristic band selection on the estimation accuracy of clay Li content,to obtain a fast and effective method for estimating clay Li content.Finally,we developed a new method for rapid and nondestructive estimation of soil lithium content.We have obtained some important results from the study.Spectral resolution exerts a significant impact on model performance,and its reduction usually leads to a decline in model performance.For the full band,the models constructed with low-order derivatives were superior to those with high-order derivatives,and the best model was obtained at the 0.4-order derivative(coefficient of determination(R^(2))and relative predictive deviation(RPD)of 0.777 and 2.118,respectively).In the characteristic bands,the lower order is sensitive to the visible-near-infrared range,and the higher order is sensitive to the short-wave infrared range,and the model constructed with the higher-order derivatives outperforms the lower-order derivatives.In this study,the combination of FOD and Random Forest(RF)can significantly improve the model performance,with R^(2),Relative Root Mean Squared Error(RRMSE),and RPD being 0.849,1.526,and 2.574,respectively.Therefore,this research provides a theoretical basis and technical reference for imaging hyperspectral exploration of anomalous areas of clay-type Li resources.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金supported by National Natural Science Foundation of China under Grant Nos.12474140 and 12347101supported by National Natural Science Foundation of China under Grant No.12204432+1 种基金supported by the graduate research and innovation foundation of Chongqing,China under Grant No.CYB25066the inaugural Doctoral Student Special Project of the China Association for Science and Technology Young Talents Lifting Program(2024)。
文摘The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Numerical simulations,such as exact diagonalization,density matrix renormalization groups,matrix product states,and Monte Carlo methods are essential for examining the properties of strongly correlated systems.Recently,density functional theory has been employed in this field within the framework of composite fermion theory.This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems,including ground state and low-energy excitations.Special attention is given to the insights provided by density functional theory regarding composite fermion behavior,edge effects,and the nature of fractional charge and magnetoroton excitations.The discussion critically examines both the advantages and limitations of these approaches,while highlighting the productive interplay between numerical simulations and theoretical models.Future directions are explored,particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.
文摘Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12571317 and 12071133).
文摘In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(Grant No.24JRRA222)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.25JRRA805).
文摘In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.
基金supported by Ajman University Internal Research Grant No.(DRGS Ref.2024-IRGHBS-3).
文摘Fractional discrete systems can enable the modeling and control of the complicated processes more adaptable through the concept of versatility by providing systemdynamics’descriptions withmore degrees of freedom.Numerical approaches have become necessary and sufficient to be addressed and employed for benefiting from the adaptability of such systems for varied applications.A variety of fractional Layla and Majnun model(LMM)system kinds has been proposed in the current work where some of these systems’key behaviors are addressed.In addition,the necessary and sufficient conditions for the stability and asymptotic stability of the fractional dynamic systems are investigated,as a result of which,the necessary requirements of the LMM to achieve constant and asymptotically steady zero resolutions are provided.As a special case,when Layla and Majnun have equal feelings,we propose an analysis of the system in view of its equilibrium and fixed point sets.Considering that the system has marginal stability if its eigenvalues have both negative and zero real portions,it is demonstrated that the system neither converges nor diverges to a steady trajectory or equilibrium point.It,rather,continues to hover along the line separating stability and instability based on the fractional LMM system.
文摘Fractional differential equations have garnered significant attention within the mathematical and physical sciences due to the diverse range of fractional operators available.Fractional calculus has demonstrated its utility across various disciplines,including biological modeling[1–5],applications in physics[6,7],most notably in the formulation of fractional diffusion equations,in robotics,and emerging areas such as intelligent artificial systems,among others.Numerous types of fractional operators exist,including those characterized by singular kernels,such as the Caputo and Riemann-Liouville derivatives[8,9].It is important to highlight that the Riemann-Liouville derivative exhibits certain limitations;most notably,the derivative of a constant is not zero,which poses a significant inconvenience.To circumvent this issue,the Caputo derivative was introduced.Additionally,there are fractional derivatives with non-singular kernels,such as the Caputo-Fabrizio derivative[10]and the Atangana-Baleanu fractional derivative[11],each providing unique advantages for modeling purposes.Given the growing interest in utilizing fractional operators for various modeling scenarios,it is imperative to propose robust methodologies for obtaining both approximate and exact solutions.Consequently,this special issue emphasizes the exploration of diverse numerical schemes aimed at deriving approximate solutions for the models under consideration.Furthermore,analytical methods have also been discussed,providing additional avenues for obtaining exact solutions.
文摘This article studies the existence and uniqueness of the mild solution of a family of control systems with a delay that are governed by the nonlinear fractional evolution differential equations in Banach spaces.Moreover,we establish the controllability of the considered system.To do so,first,we investigate the approximate controllability of the corresponding linear system.Subsequently,we prove the nonlinear system is approximately controllable if the corresponding linear system is approximately controllable.To reach the conclusions,the theory of resolvent operators,the Banach contraction mapping principle,and fixed point theorems are used.While concluding,some examples are given to demonstrate the efficacy of the proposed results.
基金Partially supported by NSFC(No.11701304)the K.C.Wong Education Foundation。
文摘In this paper we study the Freidlin-Wentzell's large deviation principle for the following nonlinear fractional stochastic heat equation driven by Gaussian noise∂/∂tu^(ε)=D_(δ)^(α)(t,x)+√εσ(u^(ε)(t,x))W(t,x),(t,x)∈[0,T]×R,where D_(δ)^(α)is a nonlocal fractional differential operator and W is the Gaussian noise which is white in time and behaves as a fractional Brownian motion with Hurst index H satisfying 3-α/4<H<1/2,in the space variable.The weak convergence approach plays an important role.
文摘Background Non-invasive computed tomography angiography(CTA)-based fractional flow reserve(CT-FFR)could become a gatekeeper to invasive coronary angiography.Deep learning(DL)-based CT-FFR has shown promise when compared to invasive FFR.To evaluate the performance of a DL-based CT-FFR technique,DeepVessel FFR(DVFFR).Methods This retrospective study was designed for iScheMia Assessment based on a Retrospective,single-center Trial of CTFFR(SMART).Patients suspected of stable coronary artery disease(CAD)and undergoing both CTA and invasive FFR examinations were consecutively selected from the Beijing Anzhen Hospital between January 1,2016 to December 30,2018.FFR obtained during invasive coronary angiography was used as the reference standard.DVFFR was calculated blindly using a DL-based CTFFR approach that utilized the complete tree structure of the coronary arteries.Results Three hundred and thirty nine patients(60.5±10.0 years and 209 men)and 414 vessels with direct invasive FFR were included in the analysis.At per-vessel level,sensitivity,specificity,accuracy,positive predictive value(PPV)and negative predictive value(NPV)of DVFFR were 94.7%,88.6%,90.8%,82.7%,and 96.7%,respectively.The area under the receiver operating characteristics curve(AUC)was 0.95 for DVFFR and 0.56 for CTA-based assessment with a significant difference(P<0.0001).At patient level,sensitivity,specificity,accuracy,PPV and NPV of DVFFR were 93.8%,88.0%,90.3%,83.0%,and 95.8%,respectively.The computation for DVFFR was fast with the average time of 22.5±1.9 s.Conclusions The results demonstrate that DVFFR was able to evaluate lesion hemodynamic significance accurately and effectively with improved diagnostic performance over CTA alone.Coronary artery disease(CAD)is a critical disease in which coronary artery luminal narrowing may result in myocardial ischemia.Early and effective assessment of myocardial ischemia is essential for optimal treatment planning so as to improve the quality of life and reduce medical costs.
基金Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120Research Council of Lithuania(LMTLT),agreement No.S-PD-24-120funded by the Research Council of Lithuania.
文摘Fractional differential equations(FDEs)provide a powerful tool for modeling systems with memory and non-local effects,but understanding their underlying structure remains a significant challenge.While numerous numerical and semi-analytical methods exist to find solutions,new approaches are needed to analyze the intrinsic properties of the FDEs themselves.This paper introduces a novel computational framework for the structural analysis of FDEs involving iterated Caputo derivatives.The methodology is based on a transformation that recasts the original FDE into an equivalent higher-order form,represented as the sum of a closed-form,integer-order component G(y)and a residual fractional power seriesΨ(x).This transformed FDE is subsequently reduced to a first-order ordinary differential equation(ODE).The primary novelty of the proposed methodology lies in treating the structure of the integer-order component G(y)not as fixed,but as a parameterizable polynomial whose coefficients can be determined via global optimization.Using particle swarm optimization,the framework identifies an optimal ODE architecture by minimizing a dual objective that balances solution accuracy against a high-fidelity reference and the magnitude of the truncated residual series.The effectiveness of the approach is demonstrated on both a linear FDE and a nonlinear fractional Riccati equation.Results demonstrate that the framework successfully identifies an optimal,low-degree polynomial ODE architecture that is not necessarily identical to the forcing function of the original FDE.This work provides a new tool for analyzing the underlying structure of FDEs and gaining deeper insights into the interplay between local and non-local dynamics in fractional systems.
基金supported by the NSFC(12131017,12221001)the National Key R&D Program of China(2022YFA1005602)。
文摘In this paper,we investigate a Dirichlet boundary value problem for a class of fractional degenerate elliptic equations on homogeneous Carnot groups G=(R^(n),o),namely{(-△_(G))^(s)u=f(x,u)+g(x,u)inΩ;u∈H_(0)^(s)(Ω),where s∈(0,1),Ω■G is a bounded open domain,(-△_(G))^(s)is the fractional sub-Laplacian,H_(0)^(s)(Ω)denotes the fractional Sobolev space,f(x,u)∈C(Ω×R),g(x,u)is a Carath′eodory function on Ω×R.Using perturbation methods and Morse index estimates in conjunction with fractional Dirichlet eigenvalue estimates,we establish the existence of multiple solutions to the problem.
文摘A Langevin delayed fractional system with multiple delays in control,is a delayed fractional system that includes delay parameters in both state and control,is first introduced.This paper is devoted to investigating the relative controllability of the Langevin delayed fractional system with multiple delays in control.For linear systems to be relatively controllable,necessary and sufficient circumstances are identified by introducing and employing the Gramian matrix.The sufficient conditions for the relative controllability of semilinear systems are ofered based on Schauder's fixed point theorem.As an unusual approach,the controllability results of the delayed system are built for the first time on the exact solution produced by the MittagLeffler type function although controllability ones in the literature are built on the Volterra integral equations or the mild solutions produced by resolvent families.
