This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables and eigenfunction expansions in time and space are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator.

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...

In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by Nigmatullin (1986), and Zaslavsky (1994) in R for modeling some physical phenomena. The fractional derivative models time delays in a diffusion process. We will give a survey of the recent results on the fractional Cauchy problem and its generalizati...

A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a ran...

This paper develops a novel boundary meshless approach, Laplace transformed boundary particle method (LTBPM), for numerical modeling of time fractional diffusion equations. It implements Laplace transform technique to obtain the corresponding time-independent inhomogeneous equation in Laplace space and then employs a truly boundary-only meshless boundary particle method (BPM) to solve this Lapl...

In this article, we deal with the inverse problem of identifying unknown source time-fractional diffusion equation in a cylinder by A fractional Landweber method. This is ill-posed. Therefore, regularization required. The main result article error between sought solution and its regularized under selection priori parameter choice rule.