About the Existence Results of Fractional Neutral Integrodifferential Inclusions with State-Dependent Delay in Fréchet Spaces

Abstract

A recent nonlinear alternative for multivalued contractions in Fréchet spaces thanks to Frigon fixed point theorem consolidated with semigroup theory is utilized to examine the existence results for fractional neutral integrodifferential inclusions (FNIDI) with state-dependent delay (SDD). An example is described to represent the hypothesis.

On the fractional differential equations with not instantaneous impulses

“…for fractional differential equations [1][2][3][4][5][6]. Moreover, impulsive fractional (partial) differential equations were widely studied due to importance in description of some processes in which sudden, discontinuous jumps occur, and general solution has been discovered for several impulsive fractional order systems in [30][31][32][33][34][35].…”