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Banded preconditioning with shift compensation for solving discrete Riesz space-fractional diffusion equations
Based on the finite-difference method, the considered Riesz space-fractional diffusion equations result in a series of linear systems, whose...
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The fractional Landweber method for identifying the space source term problem for time-space fractional diffusion equation
This paper is devoted to solve an inverse problem for identifying the source term of a time-fractional nonhomogeneous diffusion equation with a...
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A mixed virtual element method for the time-fractional fourth-order subdiffusion equation
We propose and analyze a mixed virtual element method for time-fractional fourth-order subdiffusion equation involving the Caputo fractional...
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An application of variational iteration method for solving fuzzy time-fractional diffusion equations
In this paper, an approximate solution based on the variational iteration method is given to solve the fuzzy time-fractional diffusion equations. The...
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Finite difference method for the Riesz space distributed-order advection–diffusion equation with delay in 2D: convergence and stability
In this paper, we propose numerical methods for the Riesz space distributed-order advection–diffusion equation with delay in 2D. We utilize the...
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A finite difference scheme for the two-dimensional Gray-Scott equation with fractional Laplacian
This paper studies numerical methods for the two-dimensional fractional Gray-Scott (GS) model with fractional Laplacian. A three-level linearized...
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A class of moving Kriging interpolation-based DQ methods to simulate multi-dimensional space Galilei invariant fractional advection-diffusion equation
The current work concerns to develop a new local meshless procedure to simulate the one-, two- and three-dimensional space Galilei invariant...
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Numerical Solution of Fractional Order Advection Reaction Diffusion Equation with Fibonacci Neural Network
The authors have developed an efficient method with the Fibonacci neural network’s help to solve the fractional-order reaction-diffusion equation in...
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Numerical Determination of Source from Point Observation in a Time-Fractional Boundary-Value Problem on Disjoint Intervals
In the present work, we solve numerically an inverse problem for identification of sources from point observations in a time-fractional...
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All-at-once method for variable-order time fractional diffusion equations
We propose a fast solver for the variable-order (VO) time-fractional diffusion equation. Due to the impact of the time-dependent VO function, the...
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First-Order Reaction-Diffusion System with Space-Fractional Diffusion in an Unbounded Medium
Diffusion in porous media, such as biological tissues, is characterized by deviations from the usual Fick’s diffusion laws, which can lead to...
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A fast second-order scheme for nonlinear Riesz space-fractional diffusion equations
In this paper, the fractional centered difference formula is employed to discretize the Riesz derivative, while the Crank-Nicolson scheme is...
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A novel high-order numerical scheme and its analysis for the two-dimensional time-fractional reaction-subdiffusion equation
This paper deals with the design and analysis of a high-order numerical scheme for the two-dimensional time-fractional reaction-subdiffusion...
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Improved Gegenbauer spectral tau algorithms for distributed-order time-fractional telegraph models in multi-dimensions
The distributed-order fractional telegraph models are commonly used to describe the phenomenas of diffusion and wave-like anomalous, which can model...
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Data-Driven Discovery of Time Fractional Differential Equations
In the era of data abundance and machine learning technologies, we often encounter difficulties in learning data-driven discovery of hidden physics,...
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Finite-time synchronization of complex-valued neural networks with reaction-diffusion terms: an adaptive intermittent control approach
In this paper, we present a novel approach to achieve finite-time synchronization (FTS) in a certain class of fractional-order complex-valued neural...
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An efficient fractional step numerical algorithm for time-delayed singularly perturbed 2D convection-diffusion–reaction problem with two small parameters
The manuscript contemplates a computationally robust numerical algorithm for the solution of a singularly perturbed 2D time-delayed parabolic...
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Mittag–Leffler stability of numerical solutions to time fractional ODEs
The asymptotic stable region and long-time decay rate of solutions to linear homogeneous Caputo time fractional ordinary differential equations...
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A Local Meshless Method for a Multi-term Time Fractional Non-linear Diffusion Equation
In the current work, a radial basis function based local meshless method is taken into consideration to solve the multi-term time fractional...
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A numerical solution of time-fractional mixed diffusion and diffusion-wave equation by an RBF-based meshless method
In this paper, we have developed an radial basis function (RBF) based meshless method to solve the time-fractional mixed diffusion and diffusion-wave...
