EXISTENCE AND STABILITY RESULTS OF FRACTIONAL DIFFERENTIAL EQUATIONS MITTAG-LEFFLER KERNEL

Ahsan Abbas (), Nayyar Mehmood (), AKGÃœL Ali, Inas Amacha and Thabet Abdeljawad
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Ahsan Abbas: Department of Mathematics and Statistics, International Islamic University, Sector H-10, Islamabad, Pakistan
Nayyar Mehmood: Department of Mathematics and Statistics, International Islamic University, Sector H-10, Islamabad, Pakistan
AKGÃœL Ali: Department of Mathematics, Siirt University, Art and Science Faculty, TR-56100 Siirt, Turkey3Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
Inas Amacha: Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Thabet Abdeljawad: Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia6Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-10

Abstract: This paper presents the following AB-Caputo fractional boundary value problem 0ABCDαu(ς) = 𠔖(ς,u(ς)),ς ∈ [0, 1] with integral-type boundary conditions u(0) = 0 = u″(0),γu(1) = λ∫01g 1(ϰ)u(ϰ)dϰ, of order 2 < α ≤ 3. Schauder and Krasnoselskii’s fixed point theorems are used to find existence results. Uniqueness is obtained via the Banach contraction principle. To investigate the stability of a given problem, Hyers–Ulam stability is discussed. An example is provided to validate our results.

Keywords: AB-Caputo Fractional BVP; Existence Results; Schauder Fixed Point Theorem; Uniqueness Krasnoselskii’s Fixed Point Theorem; Banach Contraction Principle and Stability (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400413

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