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q -Fractional Langevin Differential Equation with q -Fractional Integral Conditions

Author

Listed:
  • Wuyang Wang

    (Bell Honors School, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

  • Khansa Hina Khalid

    (Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan)

  • Akbar Zada

    (Department of Mathematics, University of Peshawar, Peshawar 25120, Pakistan)

  • Sana Ben Moussa

    (Faculty of Science and Arts, Mohail Asser, King Khalid University, Abha 61421, Saudi Arabia)

  • Jun Ye

    (College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

Abstract

The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q -fractional Langevin differential equation with q -fractional integral conditions. We demonstrate the existence and uniqueness of the solution to the proposed q -fractional Langevin differential equation using the Banach contraction principle and Schaefer’s fixed-point theorem. We also elaborate on different kinds of Ulam stability. The theoretical outcomes are verified by examples.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:9:p:2132-:d:1138220
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    References listed on IDEAS

    as
    1. Baleanu, Dumitru & Jajarmi, Amin & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A new study on the mathematical modelling of human liver with Caputo–Fabrizio fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. 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.
    3. Binlin Zhang & Rafia Majeed & Mehboob Alam, 2022. "On Fractional Langevin Equations with Stieltjes Integral Conditions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    4. Ntouyas, Sotiris K. & Etemad, Sina, 2015. "On the existence of solutions for fractional differential inclusions with sum and integral boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 235-243.
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