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Existence Results For Abc-Fractional Differential Equations With Non-Separated And Integral Type Of Boundary Conditions

Author

Listed:
  • 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)

  • THABET ABDELJAWAD

    (Department of Mathematics and General Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia3Department of Medical Research, China Medical University, Taichung 40402, Taiwan4Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan)

  • ALI AKGÃœL

    (Department of Mathematics, Art and Science Faculty, Siirt University, TR-56100 Siirt, Turkey)

Abstract

This paper presents a study on the existence theory of fractional differential equations involving Atangana–Baleanu (AB) derivative of order 1 < α ≤ 2, with non-separated and integral type boundary conditions. An existence result for the solutions of given AB-fractional differential equation is proved using Krasnoselskii’s fixed point theorem, while the uniqueness of the solution is obtained using Banach contraction principle. Some conditions are proposed under which the given boundary value problem is Hyers–Ulam stable. Examples are given to validate our results.

Suggested Citation

  • Nayyar Mehmood & Ahsan Abbas & Thabet Abdeljawad & Ali Akgãœl, 2021. "Existence Results For Abc-Fractional Differential Equations With Non-Separated And Integral Type Of Boundary Conditions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(05), pages 1-16, August.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:05:n:s0218348x21400168
    DOI: 10.1142/S0218348X21400168
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