A new existence results on fractional differential inclusions with state-dependent delay and Mittag-Leffler kernel in Banach space

Abstract

In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.

Keywords

• a-b fractional-order derivative
• mild solution
• fixed point theorem
• primary 26a33
• secondary 34a60