Inverse source problem for time fractional diffusion equation with Mittag-Leffler kernel

Abstract

In this work, we study the problem to identify an unknown source term for the Atangana–Baleanu fractional derivative. In general, the problem is severely ill-posed in the sense of Hadamard. We have applied the generalized Tikhonov method to regularize the instable solution of the problem. In the theoretical result, we show the error estimate between the regularized and exact solutions with a priori parameter choice rules. We present a numerical example to illustrate the theoretical result. According to this example, we show that the proposed regularization method is converged.

Determination of an Energy Source Term for Fractional Diffusion Equation

“…Maisto et al in [20] propose resolution limits for strip currents. Can et al in [21] treat the inverse problem with Mittag-Leffler. Liu et al in [22] propose a method for solving a nonlinear wave inverse energy problem.…”

Inverse problem for a nonlinear third order in time partial differential equation

“…Moreover, for this case, if the time derivative in Equation () is a fractional derivative with the order 0 < α < 1 and 1 < α < 2 , Equation () is called a fractional diffusion and diffusion‐wave equation. Direct and inverse problems for fractional partial differential equations have attracted much attention in various fields of the applied science; see previous studies 29–36 …”

Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

“…In [27] the authors applied the CF derivative to the analysis of a rock fracture process. Many other numerical and analytical techniques for the solutions of different fractional order models can be found in [28][29][30][31][32][33][34][35][36][37][38][39] and the references therein. In this work our aim is to approximate linear PDEs with the CF derivative via the Laplace transform (LT) and local meshless method.…”