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Engineering, Multidisciplinary
Yuejuan Ju, Zhiyong Liu, Jiye Yang, Qiuyan Xu
Summary: This paper applies the nonlinear variable-order fractional advection-diffusion equation to simulate complex engineering problems with time memory and space global dependence, such as anomalous diffusion. Kansa's method is used to solve the equation, where the variable order of the space fractional derivative depends on both time and space, and the variable order of the time fractional derivative is determined by space. The effectiveness and accuracy of the method are illustrated through three numerical examples.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
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Multidisciplinary Sciences
Dowlath Fathima, Muhammad Naeem, Umair Ali, Abdul Hamid Ganie, Farah Aini Abdullah
Summary: In this paper, a new approximation method is proposed for solving variable-order time-fractional modified subdiffusion equations. The complete theoretical analysis is performed and the high accuracy and feasibility of the proposed method are verified through numerical examples.
Article
Mathematics, Applied
Xian-Ming Gu, Hai-Wei Sun, Yong-Liang Zhao, Xiangcheng Zheng
Summary: This paper investigates a time-fractional diffusion equation with a time-invariant type variable fractional order. An implicit finite difference scheme is proposed to approximate the variable-order Caputo fractional derivative, while the central difference method is used for discretizing the spatial differential operator. A novel decomposition of the temporal discretization coefficients is adopted to overcome their loss of monotonicity due to the impact of the variable order, supporting the proof of convergence and unconditional stability of the numerical scheme. Numerical examples are presented to demonstrate the effectiveness of the proposed method.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Interdisciplinary Applications
Chunping Tian, Haibo Gu, Zunkai Yang
Summary: In this paper, a type of Hilfer fractional q-difference equations with nonlocal condition is investigated. The existence and uniqueness results of solutions are obtained using topological degree theory and Banach fixed point theorem. The existence of extremal solutions in an ordered Banach space is discussed using the monotone iterative method. The Ulam stability results for equations are also considered. Finally, two examples are given to illustrate the effectiveness of the theory results.
FRACTAL AND FRACTIONAL
(2023)
Article
Computer Science, Interdisciplinary Applications
Dawei Xue, Xilin Lu, Maosong Huang, Keng-Wit Lim
Summary: This study investigates the passive failure of tunnel head in strain-softening soils using a nonlocal constitutive model. It is found that the strain-softening mechanism can promote localized passive deformation and substantial ground surface movement. Key parameters such as friction angle, dilation angle, and cover depth have influences on plastic strain accumulation and ground surface deformation.
COMPUTERS AND GEOTECHNICS
(2022)
Article
Mathematics, Applied
Tran Thi Khieu, Tra Quoc Khanh
Summary: This paper investigates the problem of recovering historical distribution for diffusion equations with coupled local and nonlocal diffusion operators. It proposes a fractional filter method to achieve reliable approximations and analyzes the stability and convergence of the method. Numerical examples validate the theoretical results including ill-posedness and regularization effects.
NUMERICAL ALGORITHMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Behrouz Parsa Moghaddam, Maryam Pishbin, Zeinab Salamat Mostaghim, Olaniyi Samuel Iyiola, Alexandra Galhano, Antonio M. Lopes
Summary: A numerical technique is proposed for solving nonlocal nonlinear stochastic delayed differential equations driven by fractional variable-order Brownian noise. The method is applied to human body and Nicholson's blowfly models, and its accuracy and computational time are assessed for different values of the nonlocal order parameters. A comparison with other techniques in the literature reveals the effectiveness of the proposed scheme.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
A. Faghih, P. Mokhtary
Summary: This paper presents a new fractional Jacobi collocation method for solving a system of multi-order fractional differential equations with variable coefficients. The existence, uniqueness, and smoothness results are rigorously studied. The numerical approach includes a new interpolation operator and convergence analysis in both L-infinity and L-2 norms, with the applicability and validity of the method demonstrated through illustrative examples.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Vijay Saw, Sushil Kumar
Summary: An efficient and accurate computational scheme based on Chebyshev collocation method and finite difference approximation is proposed for solving the time-fractional convection-diffusion equation on a finite domain. The method is convenient and accurate, and its efficiency and accuracy are examined through examples and comparisons with existing methods.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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Mathematics, Applied
Mingyu He, Wenyuan Liao
Summary: This paper presents a numerical method for solving reaction-diffusion equations in spatially heterogeneous domains, which are commonly used to model biological applications. The method utilizes a fourth-order compact alternative directional implicit scheme based on Pade approximation-based operator splitting techniques. Stability analysis shows that the method is unconditionally stable, and numerical examples demonstrate its high efficiency and high order accuracy in both space and time.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Sekhar Ghosh, Dumitru Motreanu
Summary: The paper establishes the existence of infinitely many large energy solutions for a nonlocal elliptic problem involving a variable exponent fractional p(center dot)-Laplacian and a singularity, provided a positive parameter incorporated in the problem is sufficiently small. A variational method can be implemented for an associated problem obtained by truncation related to the singularity. A comparison argument allows one to pass to the original singular problem.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Article
Mathematics
Mifodijus Sapagovas, Arturas Stikonas, Olga Stikoniene
Summary: This paper deals with the numerical solution of a nonlocal boundary-value problem for a two-dimensional pseudoparabolic equation. The proposed method, a three-layer alternating direction implicit (ADI) method, generalizes Peaceman-Rachford's ADI method for the 2D parabolic equation. The stability of the method is proved using an algebraic eigenvalue problem with nonsymmetric matrices, and numerical results are presented.
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Mathematics, Applied
Yueqiang Song, Shaoyun Shi
Summary: This paper considers a class of noncooperative critical nonlocal system with variable exponents, and establishes the existence of infinitely many solutions for the problem under suitable conditions. The study relies on limit index theory and concentration-compactness principles for fractional Sobolev spaces with variable exponents.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
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Mathematics, Applied
Xiaoli Feng, Meixia Zhao, Zhi Qian
Summary: This paper addresses the backward problem of a time-space fractional diffusion equation and proposes a Tikhonov regularization method to tackle this ill-posed problem. By utilizing a-priori and a-posteriori regularization parameter choice rules, the method ensures order optimal convergence rates.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Yuru Zou, Huaxuan Hu, Jian Lu, Xiaoxia Liu, Qingtang Jiang, Guohui Song
Summary: This study introduces a new image denoising model that utilizes both fractal coding and nonlocal self-similarity priors for image compression. Experimental results demonstrate the superior performance of the model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.
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(2021)
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Mathematics, Applied
Shujun Shen, Fawang Liu, Vo V. Anh
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
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Mathematics, Applied
Yang Liu, Yanwei Du, Hong Li, Fawang Liu, Yajun Wang
NUMERICAL ALGORITHMS
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Mathematics, Applied
Ruige Chen, Fawang Liu, Vo Anh
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(2019)
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Mathematics, Applied
Zeting Liu, Fawang Liu, Fanhai Zeng
APPLIED NUMERICAL MATHEMATICS
(2019)
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Mathematics, Applied
Fawang Liu, Libo Feng, Vo Anh, Jing Li
COMPUTERS & MATHEMATICS WITH APPLICATIONS
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Mathematics, Applied
Mengchen Zhang, Ming Shen, Fawang Liu, Hongmei Zhang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
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Mathematics, Applied
Jinghua Zhang, Fawang Liu, Vo V. Anh
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2019)
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Mathematics, Applied
Libo Feng, Fawang Liu, Ian Turner
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2019)
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Mathematics, Applied
Chunyan Liu, Liancun Zheng, Mingyang Pan, Ping Lin, Fawang Liu
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
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Mathematics, Applied
Ruige Chen, Fawang Liu, Vo Anh
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2019)
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Y. H. Shi, F. Liu, Y. M. Zhao, F. L. Wang, I. Turner
APPLIED MATHEMATICAL MODELLING
(2019)
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Mathematics, Applied
Jinghua Zhang, Fawang Liu, Zeng Lin, Vo Anh
APPLIED MATHEMATICS AND COMPUTATION
(2019)
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Physics, Multidisciplinary
Chunyan Liu, Liancun Zheng, Ping Lin, Mingyang Pan, Fawang Liu
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2019)
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Mathematics, Applied
Minling Zheng, Fawang Liu, Zhengmeng Jin
APPLIED MATHEMATICS AND COMPUTATION
(2020)
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Mathematics, Applied
Libo Feng, Fawang Liu, Ian Turner
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2020)