Existence and stability results of fractional neutral integro differential equations with infinite delay

Abstract

Fractional differential equations have emerged as a highly effective tool for characterising the genetic aspects of diverse processes and have applications in numerous domains, including networks, porous media, aerodynamics, biology, medicine, ecology, and visco-elasticity. As a result, there has been a lot of research and attention focused on fractional differential equations. Recently, a number of academics have started studying novel kinds of fractional differential equations, such as those including linked, integro-differential, or neutral terms.Ulam was the first to propose the stability of functional equations . Since then, study on this type of stability has grown and developed as a driving force. When equality is substituted for inequality, which causes a perturbation of the functional equation, the idea of stability of functional equations is revealed. Stability results for fractional differential equations have been developed recently. This research aims to investigate the uniqueness and Ulam-Hyers stability of solutions for the fractional neutral functional differential equation with infinite delay, utilising the Banach contraction principle, Krasnoselskii’s theorem.