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On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

Author

Listed:
  • Chenkuan Li

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

  • Reza Saadati

    (School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran)

  • Rekha Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada)

  • Joshua Beaudin

    (Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada)

Abstract

Using Banach’s contractive principle and the Laray–Schauder fixed point theorem, we study the uniqueness and existence of solutions to a nonlinear two-term fractional integro-differential equation with the boundary condition based on Babenko’s approach and the Mittag–Leffler function. The current work also corrects major errors in the published paper dealing with a one-term differential equation. Furthermore, we provide examples to illustrate the application of our main theorems.

Suggested Citation

  • Chenkuan Li & Reza Saadati & Rekha Srivastava & Joshua Beaudin, 2022. "On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations," Mathematics, MDPI, vol. 10(12), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:1971-:d:833664
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    References listed on IDEAS

    as
    1. Wang, Xue & Luo, Danfeng & Zhu, Quanxin, 2022. "Ulam-Hyers stability of caputo type fuzzy fractional differential equations with time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Tamer Nabil, 2019. "Krasnoselskii N-Tupled Fixed Point Theorem with Applications to Fractional Nonlinear Dynamical System," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-9, March.
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    Cited by:

    1. Chenkuan Li & Reza Saadati & Joshua Beaudin & Andrii Hrytsenko, 2023. "On the Uniqueness of the Bounded Solution for the Fractional Nonlinear Partial Integro-Differential Equation with Approximations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.

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