Approximate controllability of Hilfer fractional integro-differential neutral dynamical system with infinite delay

Abstract

This paper investigates the approximate controllability of Hilfer integro-differential neutral dynamical systems with infinite delay governed by almost sectorial operators. The mild solution of the proposed system is derived using the Laplace transform technique. Subsequently, the approximate controllability of the system is established by the Bohnenblust–Karlin - fixed point theorem. Furthermore, the controllability of the associated neutral system is analyzed in detail. Finally, a numerical example is presented to demonstrate the validity and applicability of the theoretical results and our system explained via a filter system.

Keywords

approximate controllability / Hilfer fractional derivative / almost sectorial operators / multivalued maps

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