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Langevin Equation Involving Three Fractional Orders

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In this paper, the existence and uniqueness of initial value problems for nonlinear Langevin equation involving three fractional orders are discussed. We use a new norm that is convenient for the fractional and singular differential equations. This norm and the contraction mapping principles are the main tools for investigating the existence and uniqueness of the desired issue. The fractional derivatives are described in Caputo sense.

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Correspondence to Bahram Agheli.

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Communicated by Giulio Biroli.

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Darzi, R., Agheli, B. & Nieto, J.J. Langevin Equation Involving Three Fractional Orders. J Stat Phys 178, 986–995 (2020). https://doi.org/10.1007/s10955-019-02476-0

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  • Fractional Langevin equation
  • Caputo derivative
  • Existence results

Mathematics Subject Classification

  • 26A33
  • 47E05