This paper is focused on the inverse problem of identifying space-dependent source function and initial value time fractional nonhomogeneous diffusion-wave equation from noisy final measured data in a multi-dimensional case. A mollification regularization method based bilateral exponential kernel presented to solve ill-posedness for first time. Error estimates are obtained with an priori strate...

The fractional diffusion equation is derived from the master equation of continuous time random walks (CTRWs) via a straightforward application of the GnedenkoKolmogorov limit theorem. The Cauchy problem for the fractional diffusion equation is solved in various important and general cases. The meaning of the proper diffusion limit for CTRWs is discussed.

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involv...

Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion. Fractional diffusion equations employ fractional derivatives in place of the usual integer order derivatives. They govern scaling limits of random walk models, with power law jumps leading to fractional de...

in this work, we apply the radial basis functions for solving the time fractional diffusion-wave equation defined by caputo sense for                         . the problem is discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. numerical results s...

In this paper, we obtain the Sumudu transform of generalized composite fractional derivative and some lemmas related to inverse transform. Further, find solution nonlinear reaction diffusion equation with by applying Fourier transforms.

We consider initial boundary value problems for one-dimensional diffusion equation with time-fractional derivative of order α∈(0,1) which are subject to non-zero Neumann conditions. prove the uniqueness an inverse coefficient problem determining a spatially varying potential and by Dirichlet data at one end point spatial interval. The imposed conditions required be within correct Sobolev space ...

We study the inverse problem of recovering a semilinear diffusion term $a(t,\lambda)$ as well quasilinear convection $\mathcal B(t,x,\lambda,\xi)$ in nonlinear parabolic equation $$\partial_tu-\textrm{div}(a(t,u) \nabla u)+\mathcal B(t,x,u,\nabla u)\cdot\nabla u=0, \quad \mbox{in}\ (0,T)\times\Omega,$$ given knowledge flux moving quantity associated with different sources applied at boundary do...