Strong Solution and Optimal Control Problems for a Class of Fractional Linear Equations

In this paper, we examine the unique solvability (in sense of strong solutions) Cauchy problem for a linear inhomogeneous equation in Banach space solved with respect to Caputo fractional derivative. We assume that operator acting on unknown function right-hand side generates an analytic resolving family corresponding homogeneous equation. obtain representation solution and optimal control problems convex, lower semicontinuous, bounded, coercive functional considered. The general results obtained are used prove existence specific functionals. Abstract system described by illustrated examples whose special cases subdiffusion diffusion wave