LAUSR

ABSTRACT We considered two inverse source problems for a space–time fractional differential equation. Firstly recovery of a space dependent source term is studied, secondly determination of a time dependent source term is considered. A bi-orthogonal system of functions consisting of Mittag–Leffler type functions, obtained from fractional order spectral and its adjoint problem, is used to construct the solutions of the inverse source problems. Existence, uniqueness and stability results are presented for inverse problem of recovery of a space dependent source term while for time dependent source term existence and uniqueness results are proved. Some special cases for these inverse source problems are discussed.