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Solvability of a generalized ψ-Riemann–Liouville fractional BVP under nonlocal boundary conditions

Author

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  • Haddouchi, Faouzi
  • Samei, Mohammad Esmael

Abstract

In this paper we consider a class of nonlinear BVP involving fractional derivative in the ψ-Riemann–Liouville sense with nonlocal boundary conditions. By means of some properties of the Green’s function and fixed point theorems due to Banach, Boyd-Wong, and Rus, existence of a unique solution is obtained. We have some examples that prove the theory is true.

Suggested Citation

  • Haddouchi, Faouzi & Samei, Mohammad Esmael, 2024. "Solvability of a generalized ψ-Riemann–Liouville fractional BVP under nonlocal boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 355-377.
    • Handle: RePEc:eee:matcom:v:219:y:2024:i:c:p:355-377
    DOI: 10.1016/j.matcom.2023.12.029
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    References listed on IDEAS

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    1. Haidong Qu & Xuan Liu, 2015. "A Numerical Method for Solving Fractional Differential Equations by Using Neural Network," Advances in Mathematical Physics, Hindawi, vol. 2015, pages 1-12, October.
    2. Kherraz, Tahar & Benbachir, Maamar & Lakrib, Mustapha & Samei, Mohammad Esmael & Kaabar, Mohammed K.A. & Bhanotar, Shailesh A., 2023. "Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    3. Amiri, Pari & Samei, Mohammad Esmael, 2022. "Existence of Urysohn and Atangana–Baleanu fractional integral inclusion systems solutions via common fixed point of multi-valued operators," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    4. Baishya, Chandrali & Premakumari, R.N. & Samei, Mohammad Esmael & Naik, Manisha Krishna, 2023. "Chaos control of fractional order nonlinear Bloch equation by utilizing sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    Full references (including those not matched with items on IDEAS)

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