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Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ -Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition

Author

Listed:
  • Idris Ahmed

    (KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematics and Computer Science, Sule Lamido University, Kafin-Hausa, Jigawa State P.M.B 048, Nigeria)

  • Poom Kumam

    (Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, 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, Chakadara Dir(L), Khyber Pakhtunkhwa 18800, Pakistan
    Department of Mathematics and Basic Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia)

  • Piyachat Borisut

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

  • Kanokwan Sitthithakerngkiet

    (Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand)

  • Musa Ahmed Demba

    (KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Science Laboratory Building, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    Department of Mathematics, Faculty of Computing and Mathematical Sciences, Kano University of Science and Technology, Wudil, Kano State P.M.B 3244, Nigeria)

Abstract

This paper presents a class of implicit pantograph fractional differential equation with more general Riemann-Liouville fractional integral condition. A certain class of generalized fractional derivative is used to set the problem. The existence and uniqueness of the problem is obtained using Schaefer’s and Banach fixed point theorems. In addition, the Ulam-Hyers and generalized Ulam-Hyers stability of the problem are established. Finally, some examples are given to illustrative the results.

Suggested Citation

  • Idris Ahmed & Poom Kumam & Kamal Shah & Piyachat Borisut & Kanokwan Sitthithakerngkiet & Musa Ahmed Demba, 2020. "Stability Results for Implicit Fractional Pantograph Differential Equations via ϕ -Hilfer Fractional Derivative with a Nonlocal Riemann-Liouville Fractional Integral Condition," Mathematics, MDPI, vol. 8(1), pages 1-21, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:94-:d:305878
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    References listed on IDEAS

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    1. Ravichandran, C. & Logeswari, K. & Jarad, Fahd, 2019. "New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 194-200.
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