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...

In this paper, we consider the backward problem for a time fractional diffusion-wave equation in cylinder. The ill-posedness and conditional stability of inverse are proved. Based on generalized quasi-boundary value regularization method, propose an iterative method to deal with problem, has higher convergence rate. rates regularized solution under priori parameter choice rule posteriori obtain...

Abstract This paper is concerned with the inverse random source problem for a stochastic time fractional diffusion equation, where assumed to be driven by Gaussian field. The direct shown well-posed examining well-posedness and regularity of solution equivalent two-point boundary value in frequency domain. For problem, Fourier modulus coefficient proved uniquely determined variance transform da...

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...

In this paper, the inverse problem for identifying initial value of a time fractional nonhomogeneous diffusion equation in columnar symmetric region is studied. This an ill-posed problem, i.e., solution does not depend continuously on data. The Tikhonov regularization method applied to solve and obtain solution. error estimations between exact are also obtained under priori posteriori parameter...

We propose a discontinuous Galerkin method for fractional convection-diffusion equations with a superdiffusion operator of order α(1 < α < 2) defined through the fractional Laplacian. The fractional operator of order α is expressed as a composite of first order derivatives and a fractional integral of order 2 − α. The fractional convection-diffusion problem is expressed as a system of low order...