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q-Fractional Langevin Differential Equation with q-Fractional Integral Conditions
Mathematics, 2023 The major goal of this manuscript is to investigate the existence, uniqueness, and stability of a q-fractional Langevin differential equation with q-fractional integral conditions.
Wuyang Wang +4 more
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Transient aging in fractional Brownian and Langevin-equation motion [PDF]
Physical Review E, 2013 Stochastic processes driven by stationary fractional Gaussian noise, that is, fractional Brownian motion and fractional Langevin equation motion, are usually considered to be ergodic in the sense that, after an algebraic relaxation, time and ensemble averages of physical observables coincide. Recently it was demonstrated that fractional Brownian motion
Kursawe, Jochen +2 more
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Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions [PDF]
International Journal of Differential Equations, 2010 We study a Dirichlet boundary value problem for Langevin equation involving two fractional orders. Langevin equation has been widely used to describe the evolution of physical phenomena in fluctuating environments.
Bashir Ahmad, Juan J. Nieto
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Numerical simulation of the fractional Langevin equation
Thermal Science, 2012 In this paper, we study the fractional Langevin equation, whose derivative is in Caputo sense. By using the derived numerical algorithm, we obtain the displacement and the mean square displacement which describe the dynamic behaviors of the fractional Langevin equation.
Guo, Peng, Li, Changpin, Zeng, Fanhai
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On fractional Langevin equation involving two fractional orders in different intervals
Nonlinear Analysis, 2019 In this paper, we study a nonlinear Langevin equation involving two fractional orders α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness ...
Hamid Baghani, Juan J. Nieto
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Probability density of the fractional Langevin equation with reflecting walls [PDF]
Physical Review E, 2019 12 pages, 13 figures, final version as ...
Thomas Vojta +2 more
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Existence of solution for fractional Langevin equation: Variational approach [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2014 We consider the Dirichlet problem for the fractional Langevin equation with two fractional order derivatives \begin{align*} -{_{0}}D_{t}^{\alpha}(_{0}D_{t}^{\alpha}u(t)) &= f(t,u(t), {_{0}}D_{t}^{\alpha}u(t)), \quad t\in [0,1],\\ u(0) &= u(1) = 0 ...
César Torres Ledesma
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Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator
Journal of Mathematics, 2023 In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo fractional operators, with nonperiodic and nonlocal integral boundary conditions.
Sombir Dhaniya +4 more
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Advances in Mathematical Physics, 2014 We study existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Hadamard-Caputo type fractional derivatives with nonlocal fractional integral conditions. A variety of fixed point theorems are used, such as Banach’
Jessada Tariboon +2 more
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Fractal and Fractional, 2021 This research paper intends to investigate some qualitative analysis for a nonlinear Langevin integro-fractional differential equation. We investigate the sufficient conditions for the existence and uniqueness of solutions for the proposed problem using ...
Mohammed A. Almalahi +4 more
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