Existence results for neutral functional integrodifferential equations with infinite delay via fractional operators

Abstract

This paper is concerned with the existence of mild solutions for partial neutral functional integrodifferential equations with infinite delay in a Banach space. The results are obtained by using the resolvent operators and Krasnoselski-Schaefer type fixed point theorem. An example is given to illustrate the results.

Existence and Uniqueness of Mild Solutions of Stochastic Partial Integro-Differential Impulsive Equations with Infinite Delay via Resolvent Operator

“…There is a rich theory for analytic semigroups and we wish to develop theories for (1.1) which yield analytic resolvent. However, the resolvent operator does not satisfy semigroup properties (see, for instance [4,17]) and our objective in the present paper is to apply the theory developed by Grimmer [12], because it is valid for generators of strongly continuous semigroup, not necessarily analytic. The first sufficient condition proving existence and uniqueness of the mild solution is derived by utilizing Banach fixed point theorem and resolvent operator under Lipschitz continuity of nonlinear term.…”

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

“…Also, the integrodifferential systems are experienced in numerous ranges of science, the place where it is imperative to deal with aftereffect or delay (e.g., control theory, biology, ecology, and medicine). Particularly, one dependably depicts a model which has inherited qualities by integrodifferential systems in implementation; see, for instance, [23][24][25].…”

Asymptotic stability of neutral stochastic functional integro-differential equations with impulses

“…Partial integro-differential equations have wide applications in the field of mechanics, electricity, etc (see [8] for more details). For abstract models of partial integro-differential equations with resolvent operators, see for instance [3,5,8]. The deterministic model often fluctuates due to noise, and for this reason, it is sensible to use stochastic model problems instead of deterministic ones.…”