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Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel

Author

Listed:
  • 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)

  • ALI AKGÃœL

    (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)

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.

Suggested Citation

  • Ahsan Abbas & Nayyar Mehmood & Ali Akgãœl & Inas Amacha & Thabet Abdeljawad, 2024. "Existence And Stability Results Of Fractional Differential Equations Mittag-Leffler Kernel," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(07n08), pages 1-10.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:07n08:n:s0218348x24400413
    DOI: 10.1142/S0218348X24400413
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