Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach

In the present work, an inverse problem for the heat equation in two dimensional space with Robin boundary condition that involving a new fractional derivative, namely, Atangana-Baleanu approach with non-local and non-singular kernel is considered. An explicit solution set {u(x,y,t),a(t)} of the given inverse problem is obtained by using the eigenfunctions expansion method and the integral overdetermination condition. Under some assumptions the existence, uniqueness of the suggested solution, and its continuous dependence on the data are proved.