Random Fixed Point Theorems in Banach Spaces

Abstract In this paper, we establish the existence of solutions for a class of nonlinear implicit neutral fractional differential equations with terminal condition and Hilfer-Katugampola fractional derivative. The Banach contraction principle and Krasnoselskii’s fixed point theorem are used to support the arguments. An illustration is provided to demonstrate the relevance of our results.

On Nonlinear Implicit Neutral Generalized Hilfer Fractional Differential Equations with Terminal Conditions and Delay

This paper addresses some existence, attractivity and controllability results for semilinear integrodifferential equations having non-instantaneous impulsions on an infinite interval via resolvent operators in case of neutral and state-dependent delay problems. Our criteria were obtained by applying a Darbo’s fixed-point theorem combined with measures of noncompactness. The obtained result is illustrated by an example at the end.

/pdf/functional-integro-differential-equations-with-state-37ke7r1i.pdf

Functional Integro-Differential Equations with State-Dependent Delay and Non-Instantaneous Impulsions: Existence and Qualitative Results

On Implicit Impulsive Conformable Fractional Differential Equations with Infinite Delay in b-Metric Spaces

Abstract The Kirchhoff model is derived from the vibration problem of stretchable strings. This article focuses on the long-time dynamics of a class of higher-order coupled Kirchhoff systems with nonlinear strong damping. The existence and uniqueness of the solutions of these equations in different spaces are proved by prior estimation and the Faedo-Galerkin method. Subsequently, the family of global attractors of these problems is proved using the compactness theorem. In this article, we systematically propose the definition and proof process of the family of global attractors and enrich the related conclusions of higher-order coupled Kirchhoff models. The conclusions lay a theoretical foundation for future practical applications.

https://www.degruyter.com/document/doi/10.1515/dema-2022-0197/pdf

The asymptotic behaviors of solutions for higher-order (m1, m2)-coupled Kirchhoff models with nonlinear strong damping

The present paper deals with some existence results for the Darboux problem of partial fractional random differential equations with infinite delay. The arguments are based on a random fixed point theorem with stochastic domain combined with the measure of noncompactness. 

Fractional partial random differential equations with infinite delay

Abstract In the present paper we provide some existence results for the Darboux problem of partial fractional random differential equations with state-dependent delay by applying the measure of noncompactness and a random fixed point theorem with stochastic domain.

/pdf/fractional-partial-random-differential-equations-with-state-2xed89uj2d.pdf

Amel Heris

Papers

Fractional partial random differential equations with infinite delay

Fractional Partial Random Differential Equations with State-Dependent Delay