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Hilfer Fractional Quantum Derivative and Boundary Value Problems

Author

Listed:
  • Phollakrit Wongsantisuk

    (Department of Electronics Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Sotiris K. Ntouyas

    (Department of Mathematics, University of Ioannina, 451 10 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
    These authors contributed equally to this work.)

  • Donny Passary

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Jessada Tariboon

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

Abstract

In this paper, we introduce an extension of the Hilfer fractional derivative, the “Hilfer fractional quantum derivative”, and establish some of its properties. Then, we introduce and discuss initial and boundary value problems involving the Hilfer fractional quantum derivative. The existence of a unique solution of the considered problems is established via Banach’s contraction mapping principle. Examples illustrating the obtained results are also presented.

Suggested Citation

  • Phollakrit Wongsantisuk & Sotiris K. Ntouyas & Donny Passary & Jessada Tariboon, 2022. "Hilfer Fractional Quantum Derivative and Boundary Value Problems," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:878-:d:767957
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    References listed on IDEAS

    as
    1. Rujira Ouncharoen & Nichaphat Patanarapeelert & Thanin Sitthiwirattham, 2018. "Nonlocal q -Symmetric Integral Boundary Value Problem for Sequential q -Symmetric Integrodifference Equations," Mathematics, MDPI, vol. 6(11), pages 1-9, October.
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