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Existence of Solutions to a System of Fractional q -Difference Boundary Value Problems

Author

Listed:
  • Alexandru Tudorache

    (Department of Computer Science and Engineering, Gh. Asachi Technical University, 700050 Iasi, Romania)

  • Rodica Luca

    (Department of Mathematics, Gh. Asachi Technical University, 700506 Iasi, Romania)

Abstract

We are investigating the existence of solutions to a system of two fractional q -difference equations containing fractional q -integral terms, subject to multi-point boundary conditions that encompass q -derivatives and fractional q -derivatives of different orders. In our main results, we rely on various fixed point theorems, such as the Leray–Schauder nonlinear alternative, the Schaefer fixed point theorem, the Krasnosel’skii fixed point theorem for the sum of two operators, and the Banach contraction mapping principle. Finally, several examples are provided to illustrate our findings.

Suggested Citation

  • Alexandru Tudorache & Rodica Luca, 2024. "Existence of Solutions to a System of Fractional q -Difference Boundary Value Problems," Mathematics, MDPI, vol. 12(9), pages 1-24, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1335-:d:1384552
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    References listed on IDEAS

    as
    1. Chuanzhi Bai & Dandan Yang, 2020. "The Iterative Positive Solution for a System of Fractional q -Difference Equations with Four-Point Boundary Conditions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2020, pages 1-8, March.
    2. Ahmed Alsaedi & Hana Al-Hutami & Bashir Ahmad & Ravi P. Agarwal, 2022. "EXISTENCE RESULTS FOR A COUPLED SYSTEM OF NONLINEAR FRACTIONAL q-INTEGRO-DIFFERENCE EQUATIONS WITH q-INTEGRAL-COUPLED BOUNDARY CONDITIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(01), pages 1-19, February.
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