Attractive solutions for Hilfer fractional neutral stochastic integro-differential equations with almost sectorial operators

Abstract

This paper studies the integro-differential equations of Hilfer fractional (HF) neutral stochastic evolution on an infinite interval with almost sectorial operators and their attractive solutions. We use semigroup theory, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. We establish the existence and attractivity theorems for mild solutions by considering the fact that the almost sectorial operator is both compact and noncompact. Example that highlight the key findings are also provided.

Keywords

• hilfer fractional derivative
• stochastic evolution equations
• neutral systems
• infinite interval
• attractivity