Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2

Abstract

This paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order 1q2. Stochastic analysis, cosine families, fixed point theory, and fractional calculus provide the foundation of the main results. First, we explored the prospects of finding mild solutions for the Hilfer fractional stochastic differential equation. Subsequently, we determined that the specified system is approximately controllable. Finally, an example displays the theoretical application of the results.

Keywords

• approximate controllability
• hilfer fractional derivative
• multi-valued maps
• stochastic theory
• fixed point theorem