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Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders

Author

Listed:
  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Azarshahr, Tabriz, Iran)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
    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)

  • 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)

Abstract

In this paper, we study the existence of solutions for a new class of fractional q -integro-difference equations involving Riemann-Liouville q -derivatives and a q -integral of different orders, supplemented with boundary conditions containing q -integrals of different orders. The first existence result is obtained by means of Krasnoselskii’s fixed point theorem, while the second one relies on a Leray-Schauder nonlinear alternative. The uniqueness result is derived via the Banach contraction mapping principle. Finally, illustrative examples are presented to show the validity of the obtained results. The paper concludes with some interesting observations.

Suggested Citation

  • Sina Etemad & Sotiris K. Ntouyas & Bashir Ahmad, 2019. "Existence Theory for a Fractional q -Integro-Difference Equation with q -Integral Boundary Conditions of Different Orders," Mathematics, MDPI, vol. 7(8), pages 1-15, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:8:p:659-:d:251257
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    References listed on IDEAS

    as
    1. Ahmad, Bashir & Ntouyas, Sotiris K. & Tariboon, Jessada & Alsaedi, Ahmed & Alsulami, Hamed H., 2016. "Impulsive fractional q-integro-difference equations with separated boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 199-213.
    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.
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    Cited by:

    1. Shahram Rezapour & Chernet Tuge Deressa & Azhar Hussain & Sina Etemad & Reny George & Bashir Ahmad, 2022. "A Theoretical Analysis of a Fractional Multi-Dimensional System of Boundary Value Problems on the Methylpropane Graph via Fixed Point Technique," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    2. Shahram Rezapour & Sotiris K. Ntouyas & Abdelkader Amara & Sina Etemad & Jessada Tariboon, 2021. "Some Existence and Dependence Criteria of Solutions to a Fractional Integro-Differential Boundary Value Problem via the Generalized Gronwall Inequality," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    3. Shahram Rezapour & Salim Ben Chikh & Abdelkader Amara & Sotiris K. Ntouyas & Jessada Tariboon & Sina Etemad, 2021. "Existence Results for Caputo–Hadamard Nonlocal Fractional Multi-Order Boundary Value Problems," Mathematics, MDPI, vol. 9(7), pages 1-17, March.
    4. Badr Alqahtani & Saïd Abbas & Mouffak Benchohra & Sara Salem Alzaid, 2020. "Fractional q -Difference Inclusions in Banach Spaces," Mathematics, MDPI, vol. 8(1), pages 1-12, January.

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