A Three-Parameter Problem for Fractional Differential Equation with an Abstract Operator

The paper considers a nonlocal problem with three parameters for the subdiffusion equation given in abstract form. Moreover, the fractional derivative is taken in the Caputo sense and an arbitrary self-adjoint operator in a separable Hilbert space is considered as the elliptic part of the equation. Existence and uniqueness theorems are established for the solutions of the problems. Criteria ensuring the uniqueness of the solution are identified. The influence of nonlocal condition parameters on the existence and uniqueness of the solution of problems is investigated. Some of the obtained results are also new for the classical diffusion equation.