The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order β ∈ (0, 1) . The fundamental solution for the Cauchy problem is interpreted as a probability density of a selfsimilar non-Markovian stochastic process related to a phenomenon of subdiffusion (the variance grows in time sub-lin...

In many applications, such as the heat conduction and hydrology, there is a need to recover the (possibly discontinuous) diffusion coefficient a from boundary measurements of solutions of a parabolic equation. The complete inverse problem is ill posed and nonlinear, so numerical solution is quite difficult, and we linearize the problem around constant a. We study and solve numerically the linea...

A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

the determination of an unknown boundary condition, in a nonlinaer inverse diffusion problem is considered. for solving these ill-posed inverse problems, galerkin method based on sinc basis functions for space and time will be used. to solve the system of linear equation, a noise is imposed and tikhonove regularization is applied. by using a sensor located at a point in the domain of $x$, say $...

In this paper, we introduce the linear fractional self-attracting diffusion driven by a fractional Brownian motion with Hurst index 1/2 < H < 1, which is analogous to the linear self-attracting diffusion. For 1-dimensional process we study its convergence and the corresponding weighted local time. For 2-dimensional process, as a related problem, we show that the renormalized selfintersection lo...

In this paper, we consider the inverse source problem for time-fractional diffusion equation, which has been known to be an ill-posed problem. To deal with ill-posedness of problem, propose transform into a regularized L^2 and total variational (TV) regularization terms. Differing from classical Tikhonov penalty terms, TV is beneficial reconstructing discontinuous or piecewise constant solution...