Related papers: Subordination principles for the multi-dimensional…

In this paper, we investigate the initial value problem for a Caputo space-time fractional Schrodinger equation for the delta potential. To solve this equation, we use the joint Laplace transform on the spatial coordinate and the Fourier…

In this article we study inverse source problems for time-fractional diffusion equations from \textit{a posteriori} boundary measurement. Using the memory effect of these class of equations, we solve these inverse problems for several class…

This paper considers the temporal discretization of an inverse problem subject to a time fractional diffusion equation. Firstly, the convergence of the L1 scheme is established with an arbitrary sectorial operator of spectral angle $< \pi/2…

Variable-order time-fractional wave equations provide a flexible model for wave phenomena with evolving memory effects and anomalous temporal dynamics. Their numerical approximation is challenging because the variable-order fractional…

In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we…

In this paper, we investigate a fractional differential equation involving sequential Caputo derivatives, motivated by recent research on fractional models with multiple memory effects. Using techniques inspired by earlier works on…

This paper studies the linear stochastic partial differential equation of fractional orders both in time and space variables $\left(\partial^\beta + \frac{\nu}{2} (-\Delta)^{\alpha/2} \right) u(t,x)= \lambda u(t,x) \dot{W}(t,x)$, where…

This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…

The backward problem for subdiffusion equation with the fractional Riemann-Liouville time-derivative of order ? 2 (0; 1) and an arbitrary positive self-adjoint operator A is considered. This problem is ill-posed in the sense of Hadamard due…

In this paper, we focus on designing a well-conditioned Glarkin spectral methods for solving a two-sided fractional diffusion equations with drift, in which the fractional operators are defined neither in Riemann-Liouville nor Caputo sense,…

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…

Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…

In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral operator. Under a suitable transformation the variable…

In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…

The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation…

Diffusion equation with a fractional Caputo time derivative with respect to another function $g$, which defines new time scale of the process, is applied to describe anomalous diffusion of antibiotic (colistin) in a system consisting of…

In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…

In this paper, we propose a fast second-order approximation to the variable-order (VO) Caputo fractional derivative, which is developed based on $L2$-$1_\sigma$ formula and the exponential-sum-approximation technique. The fast evaluation…

This article is concerned with a semilinear time-fractional diffusion equation with a superlinear convex semilinear term in a bounded domain $\Omega$ with the homogeneous Dirichlet, Neumann, Robin boundary conditions and non-negative and…