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Hyers–Ulam’s Stability Results to a Three-Point Boundary Value Problem of Nonlinear Fractional Order Differential Equations

In: Frontiers in Functional Equations and Analytic Inequalities

Author

Listed:
  • Kamal Shah

    (University of Malakand, Department of Mathematics)

  • Zamin Gul

    (University of Malakand, Department of Mathematics)

  • Yongjin Li

    (Sun Yat-sen University, Department of Mathematics)

  • Rahmat Ali Khan

    (University of Malakand, Department of Mathematics)

Abstract

This research is devoted to investigate the existence and multiplicity results of boundary value problem (BVP) for nonlinear fractional order differential equation (FDEs). To obtain the required results, we use some fixed point theorems due to Leggett–Williams and Banach. Further in this paper, we introduce different types of Ulam’s stability concepts for the aforesaid problem of nonlinear FDEs. The concerned types of Ulam’s stability are devoted to Ulam–Hyers (UH), generalized Ulam–Hyers (GUH) stability and Ulam–Hyers–Rassias (UHR), generalized Ulam–Hyers–Rassias (GUHR) stability. Finally the whole analysis is verified by some adequate examples.

Suggested Citation

  • Kamal Shah & Zamin Gul & Yongjin Li & Rahmat Ali Khan, 2019. "Hyers–Ulam’s Stability Results to a Three-Point Boundary Value Problem of Nonlinear Fractional Order Differential Equations," Springer Books, in: George A. Anastassiou & John Michael Rassias (ed.), Frontiers in Functional Equations and Analytic Inequalities, pages 45-71, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-28950-8_3
    DOI: 10.1007/978-3-030-28950-8_3
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