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Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator

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  • Devi, Amita
  • Kumar, Anoop

Abstract

This manuscript studies the hybrid fractional differential equations (FDEs) with the p-Laplacian operator. The main aim of this research work is to establish the existence and uniqueness(EU) results as well as to analyze the Hyers-Ulam (HU) stability for hybrid FDEs involving fractional derivatives of various orders with the p-Laplacian operator. We will convert the given problem into an equivalent integral form of hybrid FDEs for EU results with the help of the green function. The existence of solution(ES) is investigated using a fixed point theorem, and the uniqueness of the solution is obtained using the Banach contraction mapping principle technique. The dynamical systems and functional analysis tools are applied to analyze the HU stability result. An example is given to demonstrate our obtained results.

Suggested Citation

  • Devi, Amita & Kumar, Anoop, 2022. "Hyers–Ulam stability and existence of solution for hybrid fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000704
    DOI: 10.1016/j.chaos.2022.111859
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    References listed on IDEAS

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    1. Khan, Aziz & Khan, Hasib & Gómez-Aguilar, J.F. & Abdeljawad, Thabet, 2019. "Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 422-427.
    2. Zidane Baitiche & Kaddour Guerbati & Mouffak Benchohra & Yong Zhou, 2019. "Boundary Value Problems for Hybrid Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 7(3), pages 1-11, March.
    3. Khan, Hasib & Jarad, Fahd & Abdeljawad, Thabet & Khan, Aziz, 2019. "A singular ABC-fractional differential equation with p-Laplacian operator," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 56-61.
    4. Khan, Aziz & Gómez-Aguilar, J.F. & Saeed Khan, Tahir & Khan, Hasib, 2019. "Stability analysis and numerical solutions of fractional order HIV/AIDS model," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 119-128.
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    1. Hasib Khan & Jehad Alzabut & Haseena Gulzar & Osman Tunç & Sandra Pinelas, 2023. "On System of Variable Order Nonlinear p-Laplacian Fractional Differential Equations with Biological Application," Mathematics, MDPI, vol. 11(8), pages 1-17, April.

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