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
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
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
In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defi...In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
In order to price European contingent claim in a class of fractional Black-Scholes market, where the prices of assets follow a Wick-Ito stochastic differential equation driven by the fractional Brownian motion and mar...In order to price European contingent claim in a class of fractional Black-Scholes market, where the prices of assets follow a Wick-Ito stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions, the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of tile fractional Brownian motion. A result about fractional Clark derivative was also obtained.展开更多
The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. I...The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.展开更多
A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional ...A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.展开更多
Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge i...Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.展开更多
In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Und...In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.展开更多
In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat eq...In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.展开更多
In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themas...In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.展开更多
The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for tho...The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.展开更多
Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are va...Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.展开更多
Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fraction...Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.展开更多
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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10972151)
文摘In this paper, we focus on studying the fractional variational principle and the differential equations of motion for a fractional mechanical system. A combined Riemann-Liouville fractional derivative operator is defined, and a fractional Hamilton principle under this definition is established. The fractional Lagrange equations and the fractional Hamilton canonical equations are derived from the fractional Hamilton principle. A number of special cases are given, showing the universality of our conclusions. At the end of the paper, an example is given to illustrate the application of the results.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
基金National Natural Science Foundation of China(No.10826098)Natural Science Foundation of Anhui Province,China(No.090416225)Anhui Natural Science Foundation of Universities,China(No.KJ2010A037)
文摘In order to price European contingent claim in a class of fractional Black-Scholes market, where the prices of assets follow a Wick-Ito stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions, the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of tile fractional Brownian motion. A result about fractional Clark derivative was also obtained.
文摘The external stability of fractional-order continuous linear control systems described by both fractional-order state space representation and fractional-order transfer function is mainly investigated in this paper. In terms of Lyapunov’s stability theory and the stability analysis of the integer-order linear control systems, the definitions of external stability for fractional-order control systems are presented. By using the theorems of the Mittag-Leffler function in two parameters, the necessary and sufficient conditions of external stability are directly derived. The illustrative examples and simulation results are also given.
基金sponsored by the National Natural Science Foundation of China(Grant No.42141010).
文摘A novel fractional elastoplastic constitutive model is proposed to accurately characterize the deformation of sandstone under true-triaxial stress states.This model is founded on the yield function and the fractional flow rule.The yield function includes parameters that govern the evolution of yield surface,enabling an accurate description of three-dimensional stress states.The direction of plastic flow is governed by the two different fractional orders,which are functions of the plastic internal variable.Additionally,a detailed process is proposed for identifying the yield function parameters and fractional orders.Subsequently,the relationship between the fractional order and the direction of plastic flow in the meridian and deviatoric planes is examined,characterized by the dilation angle and the plastic deflection angle,respectively.The non-orthogonal flow rule,also referred to as the fractional flow rule,allows for a border range of plastic deflection and dilation angles compared to the orthogonal flow rule,thereby significantly enhancing its applicability.The validity and accuracy of proposed model are verified by comparing the analytical solution of the constitutive model with the experimental data.A comparison between the non-orthogonal flow rule and orthogonal flow rule is conducted in both the deviatoric and meridian planes.The further comparison of the stress-strain curves for the non-orthogonal and orthogonal flow rules demonstrates the superiority of the fractional constitutive model.
文摘Core power is a key parameter of nuclear reactor.Traditionally,the proportional-integralderivative(PID)controllers are used to control the core power.Fractional-order PID(FOPID)controller represents the cutting edge in core power control research.In comparing with the integer-order models,fractional-order models describe the variation of core power more accurately,thus provide a comprehensive and realistic depiction for the power and state changes of reactor core.However,current fractional-order controllers cannot adjust their parameters dynamically to response the environmental changes or demands.In this paper,we aim at the stable control and dynamic responsiveness of core power.Based on the strong selflearning ability of artificial neural network(ANN),we propose a composite controller combining the ANN and FOPID controller.The FOPID controller is firstly designed and a back propagation neural network(BPNN)is then utilized to optimize the parameters of FOPID.It is shown by simulation that the composite controller enables the real-time parameter tuning via ANN and retains the advantage of FOPID controller.
基金Supported by NSFC(No.12561023)partly by the Provincial Natural Science Foundation of Jiangxi,China(Nos.20232BAB201001,20202BAB211004)。
文摘In this paper,we study the existence of least energy solutions for the following nonlinear fractional Schrodinger–Poisson system{(−∆)^(s)u+V(x)u+φu=f(u)in R^(3),(−∆)^(t)φ=u^(2)in R^(3),where s∈(3/4,1),t∈(0,1).Under some assumptions on V(x)and f,using Nehari–Pohozaev identity and the arguments of Brezis–Nirenberg,the monotonic trick and global compactness lemma,we prove the existence of a nontrivial least energy solution.
基金Partially supported by Postgraduate Research and Practice Innovation Program of Jiangsu Province(Nos.KYCX22-2211,KYCX22-2205)。
文摘In this paper,we prove the transportation cost-information inequalities on the space of continuous paths with respect to the L~2-metric and the uniform metric for the law of the mild solution to the stochastic heat equation defined on[0,T]×[0,1]driven by double-parameter fractional noise.
文摘In this paper,the fractional natural decomposition method(FNDM)is employed to find the solution for the Kundu-Eckhaus equation and coupled fractional differential equations describing the massive Thirring model.Themassive Thirring model consists of a system of two nonlinear complex differential equations,and it plays a dynamic role in quantum field theory.The fractional derivative is considered in the Caputo sense,and the projected algorithm is a graceful mixture of Adomian decomposition scheme with natural transform technique.In order to illustrate and validate the efficiency of the future technique,we analyzed projected phenomena in terms of fractional order.Moreover,the behaviour of the obtained solution has been captured for diverse fractional order.The obtained results elucidate that the projected technique is easy to implement and very effective to analyze the behaviour of complex nonlinear differential equations of fractional order arising in the connected areas of science and engineering.
文摘The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.
文摘Non-local plane elasticity problems are discussed in the context of Λ-fractional linear elasticity theory. Adapting the Λ-fractional derivative along with the Λ-fractional space, where geometry and mechanics are valid in the conventional way, non-local plane elasticity problems are solved with the help of biharmonic functions. Then, the results are transferred into the initial plane.Applications are presented to homogeneous and the fractional beam bending problem.
基金Liaoning BaiQianWan Talents Program of China(2019)National Natural Science Foundation of China(No.11547005)Natural Science Foundation of Education Department of Liaoning Province of China(2020)。
文摘Fractional or fractal calculus is everywhere and very important.It is reported that the fractal approach is suitable for insight into the effect of porous structure on thermo-properties of cloth.A novel local fractional breaking soliton equation is derived from the reduction of the linear spectral problem associated with the local fractional non-isospectral self-dual Yang-Mills equations.More specifically,the employed linear spectral problem is first reduced to the(2+1)-dimensional local fractional zero-curvature equation through variable transformations.Based on the reduced local fractional zero-curvature equation,the fractional breaking soliton equation is then constructed by the method of undetermined coefficients.This paper shows that some other local fractional models can be obtained by generalizing the existing methods of generating nonlinear partial differential equations with integer orders.
