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Fractional Langevin equation with anti-periodic boundary conditions

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  • Fazli, Hossein
  • Nieto, Juan J.

Abstract

In this work, we investigate existence and uniqueness of solutions for nonlinear Langevin equation involving two fractional orders with anti-periodic boundary conditions. Our analysis relies on the coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces. An example illustrating our approach is also discussed.

Suggested Citation

  • Fazli, Hossein & Nieto, Juan J., 2018. "Fractional Langevin equation with anti-periodic boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 332-337.
    • Handle: RePEc:eee:chsofr:v:114:y:2018:i:c:p:332-337
    DOI: 10.1016/j.chaos.2018.07.009
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    References listed on IDEAS

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    1. Jean-Philippe Bouchaud & Rama Cont, 1998. "A Langevin approach to stock market fluctuations and crashes," Science & Finance (CFM) working paper archive 500027, Science & Finance, Capital Fund Management.
    2. Bashir Ahmad & Juan J. Nieto, 2010. "Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-10, December.
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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. B. Radhakrishnan & T. Sathya, 2022. "Controllability of Hilfer Fractional Langevin Dynamical System with Impulse in an Abstract Weighted Space," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 265-281, October.
    3. S. Kabaivanov & V. Zhelinski & B. Zlatanov, 2021. "Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions," Papers 2110.01496, arXiv.org.
    4. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Ahmed Salem & Faris Alzahrani & Lamya Almaghamsi, 2019. "Fractional Langevin Equations with Nonlocal Integral Boundary Conditions," Mathematics, MDPI, vol. 7(5), pages 1-10, May.
    6. Hossein Fazli & HongGuang Sun & Juan J. Nieto, 2020. "Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited," Mathematics, MDPI, vol. 8(5), pages 1-10, May.
    7. Dumitru Baleanu & Rahmat Darzi & Bahram Agheli, 2020. "Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    8. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. 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.

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