A System of Coupled Impulsive Neutral Functional Differential Equations: New Existence Results Driven by Fractional Brownian Motion and the Wiener Process

Abdelkader Moumen, Mohamed Ferhat, Amin Benaissa Cherif, Mohamed Bouye and Mohamad Biomy ()
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Abdelkader Moumen: Department of Mathematics, College of Science, University of Ha’il, Ha’il 55473, Saudi Arabia
Mohamed Ferhat: Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir 31000, Algeria
Amin Benaissa Cherif: Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir 31000, Algeria
Mohamed Bouye: Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Mohamad Biomy: Department of Management Information Systems, College of Business Administration, Qassim University, Buraydah 52571, Saudi Arabia

Mathematics, 2023, vol. 11, issue 24, 1-23

Abstract: Conditions for the existence and uniqueness of mild solutions for a system of semilinear impulsive differential equations with infinite fractional Brownian movements and the Wiener process are established. Our approach is based on a novel application of Burton and Kirk’s fixed point theorem in extended Banach spaces. This paper aims to extend current results to a differential-inclusions scenario. The motivation of this paper for impulsive neutral differential equations is to investigate the existence of solutions for impulsive neutral differential equations with fractional Brownian motion and a Wiener process (topics that have not been considered and are the main focus of this paper).

Keywords: mathematical model; stochastic systems; wiener process; fractional derivatives; impulsive differential equations; matrix; generalized Banach space; iterative methods; differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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