Local existence for an impulsive fractional neutral integro-differential system with Riemann–Liouville fractional derivatives in a Banach space

Abstract In this manuscript, we investigate a sort of fractional neutral integro-differential equations with impulsive outcomes and extend the formula of general solutions for the impulsive fractional neutral integro-differential system in a Banach space. By using the analysis of the limit case and the operator generating compact semigroup, we derive the main results. Finally, an example is discussed to illustrate the efficiency of the results

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

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