Probability density of the fractional Langevin equation with reflecting walls.
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DOI: 10.1103/physreve.100.042142
Abstract: We investigate anomalous diffusion processes governed by the fractional Langevin equation and confined to a finite or semi-infinite interval by reflecting potential barriers. As the random and damping forces in the fractional Langevin equation fulfill… read more here.
Keywords: fractional langevin; probability density; langevin equation; reflecting walls ... See more keywords
Fractional Langevin Coupled System with Stieltjes Integral Conditions
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DOI: 10.3390/math11102278
Abstract: This article outlines the necessary requirements for a coupled system of fractional order boundary value involving the Caputo fractional derivative, including its existence, uniqueness, and various forms of Ulam stability. We demonstrate the existence and… read more here.
Keywords: system; system stieltjes; fractional langevin; langevin coupled ... See more keywords
Fractional Langevin Equations with Nonlocal Integral Boundary Conditions
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DOI: 10.3390/math7050402
Abstract: In this paper, we investigate a class of nonlinear Langevin equations involving two fractional orders with nonlocal integral and three-point boundary conditions. Using the Banach contraction principle, Krasnoselskii’s and the nonlinear alternative Leray Schauder theorems,… read more here.
Keywords: fractional langevin; integral boundary; equations nonlocal; boundary conditions ... See more keywords
Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited
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DOI: 10.3390/math8050743
Abstract: We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in… read more here.
Keywords: equation involving; langevin equation; two fractional; fractional langevin ... See more keywords