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Existence and Stability of Implicit Fractional Differential Equations with Stieltjes Boundary Conditions Involving Hadamard Derivatives

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  • Danfeng Luo
  • Mehboob Alam
  • Akbar Zada
  • Usman Riaz
  • Zhiguo Luo
  • Peter Giesl

Abstract

In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using the classical technique of functional analysis. At the end, the results are verified with the help of examples.

Suggested Citation

  • Danfeng Luo & Mehboob Alam & Akbar Zada & Usman Riaz & Zhiguo Luo & Peter Giesl, 2021. "Existence and Stability of Implicit Fractional Differential Equations with Stieltjes Boundary Conditions Involving Hadamard Derivatives," Complexity, Hindawi, vol. 2021, pages 1-36, March.
    • Handle: RePEc:hin:complx:8824935
    DOI: 10.1155/2021/8824935
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    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    3. Rafia Majeed & Binlin Zhang & Mehboob Alam, 2023. "Fractional Langevin Coupled System with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    4. Alam, Mehboob & Zada, Akbar, 2022. "Implementation of q-calculus on q-integro-differential equation involving anti-periodic boundary conditions with three criteria," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    5. Alam, Mehboob & Shah, Dildar, 2021. "Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).

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