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Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations

Author

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  • Zeeshan Ali

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

  • Poom Kumam

    (Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Kamal Shah

    (Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18800, Pakistan)

  • Akbar Zada

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan)

Abstract

This manuscript deals with the existence theory, uniqueness, and various kinds of Ulam–Hyers stability of solutions for a class and coupled system of fractional order differential equations involving Caputo derivatives. Applying Schaefer and Banach’s fixed point approaches, existence and uniqueness results are obtained for the proposed problems. Stability results are investigated by using the classical technique of nonlinear functional analysis. Examples are given with each problem to illustrate the main results.

Suggested Citation

  • Zeeshan Ali & Poom Kumam & Kamal Shah & Akbar Zada, 2019. "Investigation of Ulam Stability Results of a Coupled System of Nonlinear Implicit Fractional Differential Equations," Mathematics, MDPI, vol. 7(4), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:341-:d:221227
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    References listed on IDEAS

    as
    1. Naveed Ahmad & Zeeshan Ali & Kamal Shah & Akbar Zada & Ghaus ur Rahman, 2018. "Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations," Complexity, Hindawi, vol. 2018, pages 1-15, February.
    2. Bashir Ahmad & Juan J. Nieto, 2009. "Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-9, July.
    3. Gafiychuk, V. & Datsko, B. & Meleshko, V. & Blackmore, D., 2009. "Analysis of the solutions of coupled nonlinear fractional reaction–diffusion equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1095-1104.
    4. Nigmatullin, Raul R. & Omay, Tolga & Baleanu, Dumitru, 2010. "On fractional filtering versus conventional filtering in economics," MPRA Paper 111643, University Library of Munich, Germany.
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    Cited by:

    1. Akbar Zada & Shaheen Fatima & Zeeshan Ali & Jiafa Xu & Yujun Cui, 2019. "Stability Results for a Coupled System of Impulsive Fractional Differential Equations," Mathematics, MDPI, vol. 7(10), pages 1-29, October.
    2. Wuyang Wang & Khansa Hina Khalid & Akbar Zada & Sana Ben Moussa & Jun Ye, 2023. "q -Fractional Langevin Differential Equation with q -Fractional Integral Conditions," Mathematics, MDPI, vol. 11(9), pages 1-27, May.
    3. Ali, Zeeshan & Rabiei, Faranak & Hosseini, Kamyar, 2023. "A fractal–fractional-order modified Predator–Prey mathematical model with immigrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 466-481.

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