Inverse Problem for a Multi-Term Fractional Differential Equation

Inverse problem for a family of multi-term time fractional differential equation with non-local boundary conditions is studied. The spectral operator of the considered problem is non-self-adjoint and a bi-orthogonal set of functions is used to construct the solution. The operational calculus approach has been used to obtain the solution of the multi-term time fractional differential equations. Integral type over-determination condition is considered for unique solvability of the inverse problem. Different estimates of multinomial Mittag-Leffler functions alongside Banach fixed point theorem are used to prove the unique local existence of the solution of the inverse problem. Stability of the solution of the inverse problem on the given datum is established.