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Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions

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)

  • Ymnah Alruwaily

    (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, Ioannina 45110, Greece)

Abstract

We discuss the existence and uniqueness of solutions for a Caputo-type fractional order boundary value problem equipped with non-conjugate Riemann-Stieltjes integro-multipoint boundary conditions on an arbitrary domain. Modern tools of functional analysis are applied to obtain the main results. Examples are constructed for the illustration of the derived results. We also investigate different kinds of Ulam stability, such as Ulam-Hyers stability, generalized Ulam-Hyers stability, and Ulam-Hyers-Rassias stability for the problem at hand.

Suggested Citation

  • Bashir Ahmad & Ymnah Alruwaily & Ahmed Alsaedi & Sotiris K. Ntouyas, 2019. "Existence and Stability Results for a Fractional Order Differential Equation with Non-Conjugate Riemann-Stieltjes Integro-Multipoint Boundary Conditions," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:249-:d:212730
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    References listed on IDEAS

    as
    1. Guotao Wang & Sanyang Liu & Lihong Zhang, 2014. "Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    2. Ntouyas, Sotiris K. & Etemad, Sina, 2015. "On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 235-243.
    3. 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.
    4. Bashir Ahmad & Sotiris K. Ntouyas & Ahmed Alsaedi, 2013. "A Study of Nonlinear Fractional Differential Equations of Arbitrary Order with Riemann-Liouville Type Multistrip Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, March.
    5. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
    Full references (including those not matched with items on IDEAS)

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