Application of a tripled fixed point theorem to investigate a nonlinear system of fractional order hybrid sequential integro-differential equations-Reference-Cited by-同舟云学术

Application of a tripled fixed point theorem to investigate a nonlinear system of fractional order hybrid sequential integro-differential equations

Published:2022 Issue:10 Volume:7 Page:18708-18728
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Jamil Muhammed¹,Khan Rahmat Ali¹,Shah Kamal¹²,Abdalla Bahaaeldin²,Abdeljawad Thabet²³

Affiliation:

1. Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan

2. Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

3. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>The goal of this manuscript is to study the existence theory of solution for a nonlinear boundary value problem of tripled system of fractional order hybrid sequential integro-differential equations. The analysis depends on some results from fractional calculus and fixed point theory. As a result, we generalized Darbo's fixed point theorem to form an updated version of tripled fixed point theorem to investigate the proposed system. Also, Hyres-Ulam and generalized Hyres-Ulam stabilities results are established for the considered system. For the illustration of our main results, we provide an example.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference40 articles.

1. J. Banaś, On measures of noncompactness in Banach spaces, Comment. Math. Univ. Ca., 21 (1980), 131–143.

2. J. Banaś, M. Jleli, M. Mursaleen, B. Samet, C. Vetro, Advances in nonlinear analysis via the concept of measure of noncompactness, Singapore: Springer, 2017. https://doi.org/10.1007/978-981-10-3722-1

3. C. Corduneanu, Integral equations and applications, Cambridge: Cambridge University Press, 1991. https://doi.org/10.1017/CBO9780511569395

4. M. Jamil, R. A. Khan, K. Shah, Existence theory to a class of boundary value problems of hybrid fractional sequential integro-differential equations, Bound. Value Probl., 2019 (2019), 77. https://doi.org/10.1186/s13661-019-1190-4

5. H. Alrabaiah, M. Jamil, K. Shah, R. A. Khan, Existence theory and semi-analytical study of non-linear Volterra fractional integro-differential equations, Alex. Eng. J., 59 (2020), 4677–4686. https://doi.org/10.1016/j.aej.2020.08.025

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Qualitative analysis of tripled system of fractional Langevin equations with cyclic anti-periodic boundary conditions;Fractional Calculus and Applied Analysis;2023-09-19

2. Existence and Stability Results for Piecewise Caputo–Fabrizio Fractional Differential Equations with Mixed Delays;Fractal and Fractional;2023-08-24

3. Existence and H-U stability of a tripled system of sequential fractional differential equations with multipoint boundary conditions;Boundary Value Problems;2023-05-18

4. Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability;International Journal of Mathematics and Mathematical Sciences;2023-03-30

5. Problem on piecewise Caputo-Fabrizio fractional delay differential equation under anti-periodic boundary conditions;Physica Scripta;2023-02-08