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Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel

Author

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  • Khan, Aziz
  • Khan, Hasib
  • Gómez-Aguilar, J.F.
  • Abdeljawad, Thabet

Abstract

In this paper we are established the existence of positive solutions (EPS) and the Hyers-Ulam (HU) stability of a general class of nonlinear Atangana-Baleanu-Caputo (ABC) fractional differential equations (FDEs) with singularity and nonlinear p-Laplacian operator in Banach’s space. To find the solution for the EPS, we use the Guo-Krasnoselskii theorem. The fractional differential equation is converted into an alternative integral structure using the Atangana-Baleanu fractional integral operator. Also, HU-stability is analyzed. We include an example with specific parameters and assumptions to show the results of the proposal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:422-427
    DOI: 10.1016/j.chaos.2019.07.026
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    References listed on IDEAS

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    1. Arqub, Omar Abu & Maayah, Banan, 2018. "Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 117-124.
    2. Abu Arqub, Omar & Maayah, Banan, 2019. "Modulation of reproducing kernel Hilbert space method for numerical solutions of Riccati and Bernoulli equations in the Atangana-Baleanu fractional sense," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 163-170.
    3. Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.
    4. Wiyada Kumam & Mian Bahadur Zada & Kamal Shah & Rahmat Ali Khan, 2018. "Investigating a Coupled Hybrid System of Nonlinear Fractional Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, March.
    5. 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.
    6. 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.
    7. Saowaluck Chasreechai & Thanin Sitthiwirattham, 2018. "Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-12, January.
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    Cited by:

    1. Li, Xiaoyan, 2021. "Comment for “Existence and Hyers-Ulam stability for a nonlinear singular fractional differential equations with Mittag-Leffler kernel”," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Rhaima, Mohamed, 2023. "Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 281-295.
    3. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
    4. 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).
    5. Ain, Qura tul & Khan, Aziz & Ullah, Muhammad Irfan & Alqudah, Manar A. & Abdeljawad, Thabet, 2022. "On fractional impulsive system for methanol detoxification in human body," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    6. 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).
    7. Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Defoort, Michael & Boulaaras, Salah, 2021. "Predefined-time convergence in fractional-order systems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Ullah, Malik Zaka & Mallawi, Fouad & Baleanu, Dumitru & Alshomrani, Ali Saleh, 2020. "A new fractional study on the chaotic vibration and state-feedback control of a nonlinear suspension system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    9. 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).
    10. 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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