Controllability of coupled systems for impulsive φ-Hilfer fractional integro-differential inclusions

ABSTRACT

This paper studies the controllability of a coupled system for a class of impulsive fractional integro-differential inclusions involving φ-Hilfer fractional derivative and subject to coupled nonlocal integral initial conditions in the case of convex set-valued maps. Some auxiliary conditions are introduced in order to apply a fixed point theorem due to Bohnenblust–Karlin. An illustrative example is provided to exemplify our theoretical results.

Keywords:

• φ-Hilfer fractional derivative
• controllability results
• impulses
• integro-differential inclusions
• fixed point theorem
• coupled system
• nonlocal integral conditions

AMS (2010) Subject Classifications:

• 26A33
• 93B05
• 34A37
• 34A60
• 47H10

Disclosure statement

No potential conflict of interest was reported by the author(s).