EXISTENCE AND STABILITY RESULTS FOR COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING AB-CAPUTO DERIVATIVE-Reference-Cited by-同舟云学术

EXISTENCE AND STABILITY RESULTS FOR COUPLED SYSTEM OF FRACTIONAL DIFFERENTIAL EQUATIONS INVOLVING AB-CAPUTO DERIVATIVE

Published:2023-01 Issue:02 Volume:31 Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

MEHMOOD NAYYAR¹,ABBAS AHSAN¹,AKGÜL ALI²³⁴,ABDELJAWAD THABET⁵⁶⁷,ALQUDAH MANAR A.⁸

Affiliation:

1. Department of Mathematics and Statistics, International, Islamic University, Sector H-10, Islamabad, Pakistan

2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

3. Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey

4. Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey

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

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

7. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

8. Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

Abstract

In this paper, we use Krasnoselskii’s fixed point theorem to find existence results for the solution of the following nonlinear fractional differential equations (FDEs) for a coupled system involving AB-Caputo fractional derivative [Formula: see text] with boundary conditions [Formula: see text] We discuss uniqueness with the help of the Banach contraction principle. The criteria for Hyers–Ulam stability of given AB-Caputo fractional-coupled boundary value problem (BVP) is also discussed. Some examples are provided to validate our results. In Example 1, we find a unique and stable solution of AB-Caputo fractional-coupled BVP. In Example 2, the analysis of approximate and exact solutions with errors of nonlinear integral equations is elaborated with graphs.

Funder

Princess Nourah bint Abdulrahman University Researchers Supporting Project

Publisher

World Scientific Pub Co Pte Ltd

Subject

Applied Mathematics,Geometry and Topology,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X23400236

Reference41 articles.

1. Preface

2. Existence of chaos for partial difference equations via tangent and cotangent functions

4. An optimized Crank–Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation

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