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A singular ABC-fractional differential equation with p-Laplacian operator

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  • Khan, Hasib
  • Jarad, Fahd
  • Abdeljawad, Thabet
  • Khan, Aziz

Abstract

In this article, we have focused on the existence and uniqueness of solutions and Hyers–Ulam stability for ABC-fractional DEs with p-Laplacian operator involving spatial singularity. The existence and uniqueness of solutions are derived with the help of the well-known Guo-Krasnoselskii theorem. Our work is a continuation of the study carried out in the recently published article ” Chaos Solitons & Fractals. 2018;117:16-20.” To manifest the results, we include an example with specific parameters and assumptions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:129:y:2019:i:c:p:56-61
    DOI: 10.1016/j.chaos.2019.08.017
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    References listed on IDEAS

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    1. Abdeljawad, Thabet, 2019. "Fractional difference operators with discrete generalized Mittag–Leffler kernels," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 315-324.
    2. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
    3. Kumar, Devendra & Singh, Jagdev & Baleanu, Dumitru & Sushila,, 2018. "Analysis of regularized long-wave equation associated with a new fractional operator with Mittag-Leffler type kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 155-167.
    4. Khan, Hasib & Gómez-Aguilar, J.F. & Khan, Aziz & Khan, Tahir Saeed, 2019. "Stability analysis for fractional order advection–reaction diffusion system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 737-751.
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    Citations

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    Cited by:

    1. Tong Yuan & Hongli Yang & Ivan Ganchev Ivanov, 2021. "Reachability and Observability of Positive Linear Electrical Circuits Systems Described by Generalized Fractional Derivatives," Mathematics, MDPI, vol. 9(22), pages 1-16, November.
    2. Uroosa Arshad & Mariam Sultana & Ali Hasan Ali & Omar Bazighifan & Areej A. Al-moneef & Kamsing Nonlaopon, 2022. "Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    3. 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).
    4. 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.
    5. Khan, Hasib & Ibrahim, Muhammad & Abdel-Aty, Abdel-Haleem & Khashan, M. Motawi & Khan, Farhat Ali & Khan, Aziz, 2021. "A fractional order Covid-19 epidemic model with Mittag-Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    6. Ravichandran, C. & Logeswari, K. & Panda, Sumati Kumari & Nisar, Kottakkaran Sooppy, 2020. "On new approach of fractional derivative by Mittag-Leffler kernel to neutral integro-differential systems with impulsive conditions," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Khan, Hasib & Ahmed, Saim & Alzabut, Jehad & Azar, Ahmad Taher, 2023. "A generalized coupled system of fractional differential equations with application to finite time sliding mode control for Leukemia therapy," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    8. Logeswari, K. & Ravichandran, C., 2020. "A new exploration on existence of fractional neutral integro- differential equations in the concept of Atangana–Baleanu derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).

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