CONTROLLABILITY RESULTS FOR SOBOLEV TYPE ψ-HILFER INTEGRO-DIFFERENTIAL EQUATIONS IN HILBERT SPACE

In this paper, the approximate controllability for Sobolev type psi-Hilfer fractional backward perturbed integro-differential equations with psi- fractional non local conditions in a Hilbert space are studied. A new set of sufficient conditions are established by using semigroup theory, psi-Hilfer fractional calculus and the Schauder's fixed point theorem. The results are obtained under the assumption that the associate backward psi- fractional linear system is approximately controllable. Finally, an example is given to illustrate the obtained results.