AN INVERSE SOURCE PROBLEM FOR A GENERALIZED TIME FRACTIONAL DIFFUSION EQUATION

Abstract This paper is devoted to the study of the inverse problem of finding the time- dependent coefficient of a generalized time fractional diffusion equation, in the case of non- local boundary and integral overdetermination conditions. The existence and uniqueness of the solution of the considered inverse problem are obtained by a method based on the expan- sion of the solution by using a bi-orthogonal system of functions and the fractional calculus. Moreover, we show its continuous dependence on the data. At the end, two examples are presented to illustrate the obtained results.