Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion

Abstract

Abstract We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered system to be approximately controllable. For the main results, we use fractional calculus, stochastic analysis, fractional power of operators and Sadovskii’s fixed point theorem. At the end, an example is also given to show the applicability of our obtained theory.

Keywords

• Hilfer fractional neutral stochastic differential equations
• Nonlocal conditions
• Approximate controllability
• Fractional Brownian motion
• Noninstantaneous impulsive
• Sadovskii fixed point theorem