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Mixed Hilfer and Caputo Fractional Riemann–Stieltjes Integro-Differential Equations with Non-Separated Boundary Conditions

Author

Listed:
  • Ayub Samadi

    (Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh 5315836511, Iran)

  • Sotiris K. Ntouyas

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

  • 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)

Abstract

In this paper, we investigate a sequential fractional boundary value problem which contains a combination of Hilfer and Caputo fractional derivative operators and non-separated boundary conditions. We establish the existence of a unique solution via Banach’s fixed point theorem, while by applying Leray–Schauder’s nonlinear alternative, we prove an existence result. Finally, examples are provided to demonstrate the results obtained.

Suggested Citation

  • Ayub Samadi & Sotiris K. Ntouyas & Jessada Tariboon, 2024. "Mixed Hilfer and Caputo Fractional Riemann–Stieltjes Integro-Differential Equations with Non-Separated Boundary Conditions," Mathematics, MDPI, vol. 12(9), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1361-:d:1386397
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