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Generalized Langevin equation with a three parameter Mittag-Leffler noise

Author

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  • Sandev, Trifce
  • Tomovski, Živorad
  • Dubbeldam, Johan L.A.

Abstract

The relaxation functions for a given generalized Langevin equation in the presence of a three parameter Mittag-Leffler noise are studied analytically. The results are represented by three parameter Mittag-Leffler functions. Exact results for the velocity and displacement correlation functions of a diffusing particle are obtained by using the Laplace transform method. The asymptotic behavior of the particle in the short and long time limits are found by using the Tauberian theorems. It is shown that for large times the particle motion is subdiffusive for β−1<αδ<β, and superdiffusive for β<αδ. Many previously obtained results are recovered. Due to the many parameters contained in the noise term, the model considered in this work may be used to improve the description of data and to model anomalous diffusive processes in complex media.

Suggested Citation

  • Sandev, Trifce & Tomovski, Živorad & Dubbeldam, Johan L.A., 2011. "Generalized Langevin equation with a three parameter Mittag-Leffler noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3627-3636.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3627-3636
    DOI: 10.1016/j.physa.2011.05.039
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    Citations

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    Cited by:

    1. Trifce Sandev & Irina Petreska & Ervin K. Lenzi, 2016. "Effective Potential from the Generalized Time-Dependent Schrödinger Equation," Mathematics, MDPI, vol. 4(4), pages 1-9, September.
    2. Trifce Sandev, 2017. "Generalized Langevin Equation and the Prabhakar Derivative," Mathematics, MDPI, vol. 5(4), pages 1-11, November.
    3. Ram K. Saxena & Zivorad Tomovski & Trifce Sandev, 2015. "Analytical Solution of Generalized Space-Time Fractional Cable Equation," Mathematics, MDPI, vol. 3(2), pages 1-18, April.
    4. Baleanu, D. & Shiri, B., 2018. "Collocation methods for fractional differential equations involving non-singular kernel," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 136-145.
    5. Alexander Apelblat, 2020. "Differentiation of the Mittag-Leffler Functions with Respect to Parameters in the Laplace Transform Approach," Mathematics, MDPI, vol. 8(5), pages 1-22, April.
    6. Lini Qiu & Guitian He & Yun Peng & Huijun Lv & Yujie Tang, 2023. "Average amplitudes analysis for a phenomenological model under hydrodynamic interactions with periodic perturbation and multiplicative trichotomous noise," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(4), pages 1-20, April.
    7. Pece Trajanovski & Petar Jolakoski & Ljupco Kocarev & Trifce Sandev, 2023. "Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting," Mathematics, MDPI, vol. 11(16), pages 1-28, August.

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