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Existence Results For Multi-Term Fractional Differential Equations With Nonlocal Boundary Conditions Involving Atangana–Baleanu Derivative

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 Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon3Department of Mathematics, Faculty of Arts and Sciences, Siirt University, 56100 Siirt, Turkey4Mathematics Research Center, Department of Mathematics, Faculty of Arts and Sciences, Near East University, Near East Boulevard, 99138 Nicosia/TRNC Mersin 10, Turkey)

  • 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)

Abstract

In this paper, the existence results for the solutions of the multi-term ABC-fractional differential boundary value problem (BVP) (δ20ABCDα+2 + δ 10ABCDα+1 + δ 00ABCDα)x(t) = ζ(t,x(t)) of order 0 < α < 1 with nonlocal boundary conditions have been derived by using Krasnoselskii’s fixed point theorem. The uniqueness of the solution is obtained with the help of Banach contraction principle. Examples are provided to confirm our obtained results.

Suggested Citation

  • Ahsan Abbas & Nayyar Mehmood & Ali Akgãœl & Thabet Abdeljawad & Manar A. Alqudah, 2023. "Existence Results For Multi-Term Fractional Differential Equations With Nonlocal Boundary Conditions Involving Atangana–Baleanu Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-19.
  • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400248
    DOI: 10.1142/S0218348X23400248
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    Cited by:

    1. Lazebnik, Teddy & Bunimovich-Mendrazitsky, Svetlana & Kiselyov, Alex, 2023. "Mathematical model for BCG-based treatment of type 1 diabetes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).

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