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

Nayyar Mehmood (), Ahsan Abbas (), AKGÃœL Ali, Thabet Abdeljawad and Manar A. Alqudah ()
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Nayyar Mehmood: Department of Mathematics and Statistics, International, Islamic University, Sector H-10, Islamabad, Pakistan
Ahsan Abbas: Department of Mathematics and Statistics, International, Islamic University, Sector H-10, Islamabad, Pakistan
AKGÃœL Ali: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon3Department of Mathematics, Art and Science Faculty, Siirt University, 56100 Siirt, Turkey4Department of Mathematics, Mathematics Research Center, Near East University, Near East Boulevard, PC
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia6Department of Medical Research, China Medical University, Taichung 40402, Taiwan7Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea
Manar A. Alqudah: Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh 11671, Saudi Arabia

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-16

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 0ABCDα𠜗(ℓ) = ζ(ℓ,𠜗(ℓ),℘(ℓ)),1 < α ≤ 2,0ABCDσ℘(ℓ) = ξ(ℓ,𠜗(ℓ),℘(ℓ)),1 < σ ≤ 2,for allℓ ∈ [0, 1], with boundary conditions 𠜗(0) = 0,λ𠜗′(η) = γ𠜗′(1),℘(0) = 0,λ℘′(η) = γ℘′(1). 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.

Keywords: Coupled System; AB-Caputo Fractional BVP; Existence; Uniqueness; Krasnoselskii’s Fixed Point Theorem; Banach Contraction Principle; Stability (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400236

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