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

Author

Listed:
  • 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
    Department of Mathematics and Computer Science, Faculty of Science, Port Said University, Port Said 42511, Egypt)

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).

Suggested Citation

  • Abdelkader Moumen & Mohamed Ferhat & Amin Benaissa Cherif & Mohamed Bouye & Mohamad Biomy, 2023. "A System of Coupled Impulsive Neutral Functional Differential Equations: New Existence Results Driven by Fractional Brownian Motion and the Wiener Process," Mathematics, MDPI, vol. 11(24), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4949-:d:1299667
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    References listed on IDEAS

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    1. Svetlin G. Georgiev & Khaled Zennir & Wiem Abedelmonem Salah Ben Khalifa & Amal Hassan Mohammed Yassin & Aymen Ghilen & Sulima Ahmed Mohammed Zubair & Najla Elzein Abukaswi Osman, 2022. "Classical Solutions For A Bvp For A Class Impulsive Fractional Partial Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-12, December.
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