Analysis of Backward Source Problems for Some Fractional Order Differential Equations

Abstract

In this article, we intend to look at certain backward source problems for Fractional Differential Equations (FDEs) with Robin boundary conditions, by considering a bi-ordinal Hilfer fractional derivative  of order  and  of type  (for both space and time). We show that the backward problem is well-posed by expanding the eigenfunctions of a spectral problem and using the generalized Fourier method.