An inverse source problem for a two terms time-fractional diffusion equation

Abstract

In this paper, we consider an inverse problem for a linear heat equation involving two time-fractional derivatives, subject to a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution with an over- determining function of integral type.

Anomalous Diffusion with Caputo-Fabrizio Time Derivative: an Inverse Problem.

“…In [27] there is a complete list of references where identification of various type of sources are listed. The case of fractional diffusion equation was studied in [3,15,25,26,29,36], among others. Separable source terms of the form h(t)s(x) arise in various physical model; for example, the heat process of radioactive decay [19], and have been extensively studied.…”

Unraveling forward and backward source problems for a nonlocal integrodifferential equation: A journey through operational calculus for Dzherbashian‐Nersesian operator

“…These kind of problems have also been studied for fractional diffusion equations in [16][17][18]. Recently, backward problems for FDEs involving Caputo and generalized Riemann-Liouville derivatives have been extensively studied [19][20][21]. However, there is a limited body of literature pertaining to the forward and backward problems associated with FDEs that feature the Dzherbashian-Nersesian operator.…”