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Hyers–Ulam stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives

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  • Alam, Mehboob
  • Shah, Dildar

Abstract

In this article, we investigate the existence, uniqueness, and stability of coupled implicit fractional integro-differential equations with Riemann–Liouville derivatives. We analyze the existence and uniqueness of the projected model with the help of Banach contraction principle, Schauder’s fixed point theorem, and Krasnoselskii’s fixed point theorem. Moreover, we present different types of stability using the classical technique of functional analysis. To illustrate our theoretical results, at the end we give an example.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004768
    DOI: 10.1016/j.chaos.2021.111122
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    References listed on IDEAS

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    1. 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.
    2. Shah, Syed Omar & Zada, Akbar, 2019. "Existence, uniqueness and stability of solution to mixed integral dynamic systems with instantaneous and noninstantaneous impulses on time scales," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 202-213.
    3. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    4. Usman Riaz & Akbar Zada & Zeeshan Ali & Manzoor Ahmad & Jiafa Xu & Zhengqing Fu, 2019. "Analysis of Nonlinear Coupled Systems of Impulsive Fractional Differential Equations with Hadamard Derivatives," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-20, June.
    5. Arshad Ali & Vidushi Gupta & Thabet Abdeljawad & Kamal Shah & Fahd Jarad, 2020. "Mathematical Analysis of Nonlocal Implicit Impulsive Problem under Caputo Fractional Boundary Conditions," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, November.
    6. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
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    Cited by:

    1. Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2022. "Fuzzy-weighted differential evolution computing paradigm for fractional order nonlinear wiener systems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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