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Nonlinear Integro-Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals with Nonlocal Boundary Data

Author

Listed:
  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Abrar Broom

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ahmed Alsaedi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Sotiris K. Ntouyas

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece)

Abstract

In this paper, we study the existence of solutions for a new nonlocal boundary value problem of integro-differential equations involving mixed left and right Caputo and Riemann–Liouville fractional derivatives and Riemann–Liouville fractional integrals of different orders. Our results rely on the standard tools of functional analysis. Examples are constructed to demonstrate the application of the derived results.

Suggested Citation

  • Bashir Ahmad & Abrar Broom & Ahmed Alsaedi & Sotiris K. Ntouyas, 2020. "Nonlinear Integro-Differential Equations Involving Mixed Right and Left Fractional Derivatives and Integrals with Nonlocal Boundary Data," Mathematics, MDPI, vol. 8(3), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:336-:d:327877
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    References listed on IDEAS

    as
    1. Peng, Li & Zhou, Yong, 2015. "Bifurcation from interval and positive solutions of the three-point boundary value problem for fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 458-466.
    2. Ahmad, Bashir & Luca, Rodica, 2018. "Existence of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 516-534.
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