Abstract
In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, \(D^{\alpha,\beta}u(t)+Au(t)=f(t)\) ( \(0<\alpha<1\) , \(0\leq\beta\leq 1\) and \(0<t\leq T\) ), \(I^{\delta}u(t)=\gamma I^{\delta}u(+0)+\varphi\) ( \(\gamma\) is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator \(A\) , is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.
