This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.

Abstract This paper is devoted to the inverse problem of determining spatially dependent source in a time fractional diffusion-wave equation, with aid extra measurement data at subboundary. A uniqueness result obtained by using analyticity and newly established unique continuation principle provided that coefficients are all temporally independent. We also derive Lipschitz stability our under s...

In this article, we study inverse source problems for time-fractional diffusion equations from a posteriori boundary measurement. Using the memory effect of these class equations, solve several space- or time-dependent terms. We prove also unique determination general space–time-dependent separated variables terms such Our approach is based on singularities Laplace transform in time traces solu...

We consider a fractional diffusion equation (FDE) = a D u a t u C t xx ( ) with an undetermined time-dependent diffusion coefficient a(t). Firstly, for the direct problem part, we establish the existence, uniqueness and some regularity properties of the weak solution for this FDE with a fixed a t . ( ) Secondly, for the inverse problem part, in order to recover a t , ( ) we introduce an operato...

  In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...

Fractional diffusion equations are abstract partial differential equations that involve fractional derivatives in space and time. They are useful to model anomalous diffusion, where a plume of particles spreads in a different manner than the classical diffusion equation predicts. An initial value problem involving a space-fractional diffusion equation is an abstract Cauchy problem, whose analyt...