In this paper,a new temporal-spatial fractional order model is proposed to study the dynamic behavior of thermo-viscoelastic nanoplates.Traditional singular kernel in Caputo fractional order differentiation is replace...In this paper,a new temporal-spatial fractional order model is proposed to study the dynamic behavior of thermo-viscoelastic nanoplates.Traditional singular kernel in Caputo fractional order differentiation is replaced by the non-singular kernel and thus leads to a new generalized fractional order differential model with the integer order differential models as a special case.This improved model can more flexibly describe small-scale mechanical behavior and time-dependent heat conduction behavior and provides a clear physical explanation for the fractional order parameters.Spatial nonlocal effects are described in terms of nonlocal strain gradient elasticity and spatial fractional order derivatives,while the time-dependent effects are described in terms of non-Fourier heat conduction,viscoelasticity,and time fractional order derivatives.In addition,it is the first time that the nonlocal characteristic lengths and the memory characteristic times are introduced as two new small-scale parameters in the fractional order derivatives of non-singular kernels to focus on the short-range nonlocal behaviors and the short-term memory behaviors.Numerical examples of the free vibration and the forced vibration under step loading are given,and the effects of the spatial fractional order parameter and the temporal fractional order parameter are both discussed.展开更多
In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, thi...In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown Hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated.展开更多
The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg...The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation(LMB)neural networks(NNs),i.e.,LMBNNs.The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics,healthy hepatocytes(H),capsids(D),infected hepatocytes(I),free virus(V)and antibodies(W).The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS.The data magnitudes are implemented 75%for training,10%for certification and 15%for testing to solve the FO-HBV-DIS with the response of antibody immune.The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach.To authenticate the validity,competence,consistency,capability and exactness of the LMBNNs,the numerical presentations using the mean square error(MSE),error histograms(EHs),state transitions(STs),correlation and regression are accomplished.展开更多
Medical imaging is essential for modern cancer screening and diagnosis,but image quality is usually compro-mised in an attempt to lower patient risk.Traditional computer-aided diagnosis(CAD)systems that employ anomaly...Medical imaging is essential for modern cancer screening and diagnosis,but image quality is usually compro-mised in an attempt to lower patient risk.Traditional computer-aided diagnosis(CAD)systems that employ anomaly detection techniques have increased diagnostic accuracy by assisting radiologists in interpreting medical images.However,existing problems like inconsistent pixel values,computational inefficiencies,and limited generalizability hinder the successful application of AI-based models in real-time clinical settings.Due to distinct pixel intensity variation,medical images necessitate specific transformation;however,model develop-ment is complicated by the lack of standard parameter guidelines.Current models'high memory and processing requirements restrict their applicability in settings with limited resources,especially in rural areas.The need for a solution that ensures both diagnostic accuracy and computational efficiency is further highlighted by the fact that noise and artifacts in low-resolution images make it more difficult to diagnose diseases accurately.This study presents a method to improving the quality of medical images by using a non-convex fractional differential equation(NC-FODE).Pixel strength is efficiently calculated by NC-FODE to increase intensity and improve diagnostic relevance.To ensure precise and adaptable parameter setting for different image modalities,a dual supervised neural network(DsNN)is utilized to approximate partial derivatives and set upper bounds for model parameters.Using publicly available radiography datasets,it has been demonstrated that the proposed method greatly enhances image quality across a range of imaging modalities without requiring extensive pre-processing.Real-time processing appropriate for hectic clinical settings is made possible by experimental results showing improved pixel density,decreased noise,and superior computational efficiency.It can be customized for variety of clinical applications since it ensures consistency and reproducibility across different imaging datasets.展开更多
Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, et...Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.展开更多
In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.
This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient ...This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).展开更多
The present work encompasses a new image enhancement algorithm using newly constructed Chebyshev fractional order differentiator. We have used Chebyshev polynomials to design Chebyshev fractional order differentiator....The present work encompasses a new image enhancement algorithm using newly constructed Chebyshev fractional order differentiator. We have used Chebyshev polynomials to design Chebyshev fractional order differentiator. We have generated the high pass filter corresponding to it. The designed filters are applied for decomposing the input image into four bands and low-low(L-L) sub-band is updated using correction coefficients. Reconstructed image with updated L-L sub-band provides the enhanced image. The visual results obtained are encouraging for image enhancement. The applicability of the developed algorithm is illustrated on three different test images.The effects of order of differentiation on the edges of images have also been presented and discussed.展开更多
A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions...A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations.展开更多
Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072022 and 11872105)Fundamental Research Funds for the Central Universities(Grant Nos.FRF-TW-2018-005 and FRF-BR-18-008B).
文摘In this paper,a new temporal-spatial fractional order model is proposed to study the dynamic behavior of thermo-viscoelastic nanoplates.Traditional singular kernel in Caputo fractional order differentiation is replaced by the non-singular kernel and thus leads to a new generalized fractional order differential model with the integer order differential models as a special case.This improved model can more flexibly describe small-scale mechanical behavior and time-dependent heat conduction behavior and provides a clear physical explanation for the fractional order parameters.Spatial nonlocal effects are described in terms of nonlocal strain gradient elasticity and spatial fractional order derivatives,while the time-dependent effects are described in terms of non-Fourier heat conduction,viscoelasticity,and time fractional order derivatives.In addition,it is the first time that the nonlocal characteristic lengths and the memory characteristic times are introduced as two new small-scale parameters in the fractional order derivatives of non-singular kernels to focus on the short-range nonlocal behaviors and the short-term memory behaviors.Numerical examples of the free vibration and the forced vibration under step loading are given,and the effects of the spatial fractional order parameter and the temporal fractional order parameter are both discussed.
文摘In this study, we establish an approximate method which produces an approximate Hermite polynomial solution to a system of fractional order differential equations with variable coefficients. At collocation points, this method converts the mentioned system into a matrix equation which corresponds to a system of linear equations with unknown Hermite polynomial coefficients. Construction of the method on the aforementioned type of equations has been presented and tested on some numerical examples. Results related to the effectiveness and reliability of the method have been illustrated.
基金the Program Management Unit for Human Resources&Institutional Development,Research and Innovation(grant number B05F640092).
文摘The current investigations are presented to solve the fractional order HBV differential infection system(FO-HBV-DIS)with the response of antibody immune using the optimization based stochastic schemes of the Levenberg-Marquardt backpropagation(LMB)neural networks(NNs),i.e.,LMBNNs.The FO-HBV-DIS with the response of antibody immune is categorized into five dynamics,healthy hepatocytes(H),capsids(D),infected hepatocytes(I),free virus(V)and antibodies(W).The investigations for three different FO variants have been tested numerically to solve the nonlinear FO-HBV-DIS.The data magnitudes are implemented 75%for training,10%for certification and 15%for testing to solve the FO-HBV-DIS with the response of antibody immune.The numerical observations are achieved using the stochastic LMBNNs procedures for soling the FO-HBV-DIS with the response of antibody immune and comparison of the results is presented through the database Adams-Bashforth-Moulton approach.To authenticate the validity,competence,consistency,capability and exactness of the LMBNNs,the numerical presentations using the mean square error(MSE),error histograms(EHs),state transitions(STs),correlation and regression are accomplished.
文摘Medical imaging is essential for modern cancer screening and diagnosis,but image quality is usually compro-mised in an attempt to lower patient risk.Traditional computer-aided diagnosis(CAD)systems that employ anomaly detection techniques have increased diagnostic accuracy by assisting radiologists in interpreting medical images.However,existing problems like inconsistent pixel values,computational inefficiencies,and limited generalizability hinder the successful application of AI-based models in real-time clinical settings.Due to distinct pixel intensity variation,medical images necessitate specific transformation;however,model develop-ment is complicated by the lack of standard parameter guidelines.Current models'high memory and processing requirements restrict their applicability in settings with limited resources,especially in rural areas.The need for a solution that ensures both diagnostic accuracy and computational efficiency is further highlighted by the fact that noise and artifacts in low-resolution images make it more difficult to diagnose diseases accurately.This study presents a method to improving the quality of medical images by using a non-convex fractional differential equation(NC-FODE).Pixel strength is efficiently calculated by NC-FODE to increase intensity and improve diagnostic relevance.To ensure precise and adaptable parameter setting for different image modalities,a dual supervised neural network(DsNN)is utilized to approximate partial derivatives and set upper bounds for model parameters.Using publicly available radiography datasets,it has been demonstrated that the proposed method greatly enhances image quality across a range of imaging modalities without requiring extensive pre-processing.Real-time processing appropriate for hectic clinical settings is made possible by experimental results showing improved pixel density,decreased noise,and superior computational efficiency.It can be customized for variety of clinical applications since it ensures consistency and reproducibility across different imaging datasets.
文摘Fractional-order time-delay differential equations can describe many complex physical phenomena with memory or delay effects, which are widely used in the fields of cell biology, control systems, signal processing, etc. Therefore, it is of great significance to study fractional-order time-delay differential equations. In this paper, we discuss a finite volume element method for a class of fractional-order neutral time-delay differential equations. By introducing an intermediate variable, the fourth-order problem is transformed into a system of equations consisting of two second-order partial differential equations. The L1 formula is used to approximate the time fractional order derivative terms, and the finite volume element method is used in space. A fully discrete format of the equations is established, and we prove the existence, uniqueness, convergence and stability of the solution. Finally, the validity of the format is verified by numerical examples.
基金supported by the National Natural Science Foundation of China(No.11071001)the Natural Science Foundation of Huangshan University(No.2010xkj014)the Foundation of Education Department of Anhui Province(KJ2011B167)
文摘In this paper,we use the analytic semigroup theory of linear operators and fixed point method to prove the existence of mild solutions to a semilinear fractional order functional differential equations in a Banach space.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12071229,12101452)Tianjin Normal University Doctoral Research Project(Grant No.52XB2110)。
文摘This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system{div A(x-Du)-■π=divF,inΩdivu=0,inΩ.In terms of the difference quotient method,our first result reveals that if F∈B_(p,q.loc)^(β)(Ω,R^(n))for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressureπwith no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vector field A(x,Du)is simplified to the full gradient■u,we improve the aforementioned Besov regularity for all integrability exponents p and q by establishing a new Campanato-type decay estimates for(■u,π).
文摘The present work encompasses a new image enhancement algorithm using newly constructed Chebyshev fractional order differentiator. We have used Chebyshev polynomials to design Chebyshev fractional order differentiator. We have generated the high pass filter corresponding to it. The designed filters are applied for decomposing the input image into four bands and low-low(L-L) sub-band is updated using correction coefficients. Reconstructed image with updated L-L sub-band provides the enhanced image. The visual results obtained are encouraging for image enhancement. The applicability of the developed algorithm is illustrated on three different test images.The effects of order of differentiation on the edges of images have also been presented and discussed.
文摘A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations.
文摘Using a fixed point theorem,this paper discusses the existence and uniqueness of positive solutions to a system of nonlinear delay fractional differential equations and obtains some new results.
