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The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral

Author

Listed:
  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Madeaha Alghanmi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Ahmed Alsaedi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

  • Hari M. Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan)

  • Sotiris K. Ntouyas

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece)

Abstract

In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary conditions involving a generalized integral operator. The modern techniques of functional analysis are employed to obtain the desired results. The paper concludes with illustrative examples.

Suggested Citation

  • Bashir Ahmad & Madeaha Alghanmi & Ahmed Alsaedi & Hari M. Srivastava & Sotiris K. Ntouyas, 2019. "The Langevin Equation in Terms of Generalized Liouville–Caputo Derivatives with Nonlocal Boundary Conditions Involving a Generalized Fractional Integral," Mathematics, MDPI, vol. 7(6), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:533-:d:238850
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    References listed on IDEAS

    as
    1. Fazli, Hossein & Nieto, Juan J., 2018. "Fractional Langevin equation with anti-periodic boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 332-337.
    2. Javidi, Mohammad & Ahmad, Bashir, 2015. "Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system," Ecological Modelling, Elsevier, vol. 318(C), pages 8-18.
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    Cited by:

    1. Ahmed Alsaedi & Bashir Ahmad & Madeaha Alghanmi & Sotiris K. Ntouyas, 2019. "On a Generalized Langevin Type Nonlocal Fractional Integral Multivalued Problem," Mathematics, MDPI, vol. 7(11), pages 1-13, October.
    2. Ahmed Salem & Kholoud N. Alharbi & Hashim M. Alshehri, 2022. "Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space," Mathematics, MDPI, vol. 10(8), pages 1-17, April.

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