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Mixed stochastic heat equation with fractional Laplacian and gradient perturbation
We introduce a new stochastic heat equation with a mixed operator, which is a combination of the standard Laplacian, a fractional Laplacian and the...
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An ADMM approach to a TV model for identifying two coefficients in the time-fractional diffusion system
This paper is devoted to the theoretical and numerical study of an inverse identification problem of two unknown space-dependent coefficients for a...
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Analytical solution of non-linear fractional diffusion equation
In this paper, we obtain an approximate/analytical solution of nonlinear fractional diffusion equation using the q-homotopy analysis transform...
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A novel robust fractional-time anisotropic diffusion for multi-frame image super-resolution
In this paper, we propose an image multi-frame Super Resolution (SR) method based on fractional-time Caputo derivative combined with Weickert-type...
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An RBF Based Finite Difference Method for the Numerical Approximation of Multi-term Nonlinear Time Fractional Two Dimensional Diffusion-Wave Equation
The main goal of this manuscript is to develop an RBF-based meshfree method to solve the multi-term time-fractional nonlinear two-dimensional...
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Numerical framework for the Caputo time-fractional diffusion equation with fourth order derivative in space
A finite difference scheme along with a fourth-order approximation is examined in this article for finding the solution of time-fractional diffusion...
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Inverse source problem for a space-time fractional diffusion equation
This paper is concerned with an inverse source problem for a space-time fractional diffusion equation. We aim to identify an unknown source term from...
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A Difference Scheme with Intrinsic Parallelism for Fractional Diffusion-wave Equation with Dam**
Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific...
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Recovering the temperature distribution for multi-term time-fractional sideways diffusion equations
In the current paper, an inverse boundary value problem so-called the sideways problem for the multi-term time-fractional diffusion equation is...
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Direct Method of Moving Planes for Tempered Fractional Laplacian Equations
In this paper, we extend the direct method of moving planes to tempered fractional Laplacian equations. To carry out the method, a narrow region...
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On numerical simulations of time fractional Phi-four equation using Caputo derivative
The fractional model which played an essential role in nuclear and particle physics used to describe the nuclear element interaction is the Phi-four...
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Discretization and Analysis of an Optimal Control of a Variable-Order Time-Fractional Diffusion Equation with Pointwise Constraints
We prove the well-posedness and regularity of an optimal control model with pointwise constraints governed by a variable-order Caputo time-fractional...
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An Adaptive Memory method for Accurate and Efficient Computation of the Caputo Fractional Derivative
A fractional derivative is a temporally nonlocal operation which is computationally intensive due to inclusion of the accumulated contribution of...
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Error Estimate of Finite Element Approximation for Two-Sided Space-Fractional Evolution Equation with Variable Coefficient
In this paper, we develop and analyze a finite element method (FEM) for a one-dimensional two-sided time-dependent space-fractional diffusion...
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Nonlocal Diffusion Models with Consistent Local and Fractional Limits
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter...
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Numerical Analysis of a Fast Finite Element Method for a Hidden-Memory Variable-Order Time-Fractional Diffusion Equation
We investigate a fast finite element scheme to a hidden-memory variable-order time-fractional diffusion equation. Different from the traditional L1...
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Solving Distributed-Order Fractional Equations by LS-SVR
Over the past years, several artificial intelligence methods have been developed for solving various types of differential equations; due to their...
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The direct and inverse problem for sub-diffusion equations with a generalized impedance subregion
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume...
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Fractional models for analysis of economic risks
In this review paper we try to describe some recent results on modeling and analysis of economic risks by using the techniques of fractional...