Existence and uniqueness results for a multi-parameters nonlocal diffusion equation

This paper is devoted to identifying a time-dependent source term for a multi-term time-fractional diffusion equation with a nonlocal dynamic boundary and integral type over-determination condition. The time-fractional derivatives are considered in Caputo's sense. By applying Fourier's method we obtained multi-term ordinary fractional order differential equation which has been reduced to an algebraic equation by using Laplace transform. Inverse Laplace transform is used to obtain the solution of multi-term ordinary fractional order differential equation which involves multinomial Mittag-Leffler functions. Under some regularity and consistency conditions on the data, unique existence and stability of the regular solution of the inverse problem is proved.