Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited [PDF]
Mathematics, 2020 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
Hossein Fazli +2 more
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On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation [PDF]
Advances in Mathematical Physics, 2020 In this work, we give sufficient conditions to investigate the existence and uniqueness of solution to fractional-order Langevin equation involving two distinct fractional orders with unprecedented conditions (three-point boundary conditions including ...
Ahmed Salem, Noorah Mshary
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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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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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Axioms, 2022 The fractional Langevin equation has more advantages than its classical equation in representing the random motion of Brownian particles in complex viscoelastic fluid.
Kaihong Zhao
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Fractal and Fractional, 2022 The fractional Langevin equation is a very effective mathematical model for depicting the random motion of particles in complex viscous elastic liquids. This manuscript is mainly concerned with a class of nonlinear fractional Langevin equations involving
Kaihong Zhao
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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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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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On a Nonlinear Fractional Langevin Equation of Two Fractional Orders with a Multiplicative Noise
Fractal and Fractional, 2022 We consider a stochastic nonlinear fractional Langevin equation of two fractional orders Dβ(Dα+γ)ψ(t)=λϑ(t,ψ(t))w˙(t),0<t≤1. Given some suitable conditions on the above parameters, we prove the existence and uniqueness of the mild solution to the ...
Mcsylvester Ejighikeme Omaba +1 more
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Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions [PDF]
Boundary Value Problems, 2011 We study a boundary value problem to Langevin equation involving two fractional orders. The Banach fixed point theorem and Krasnoselskii's fixed point theorem are applied to establish the existence results.
Chen Yi, Chen Anping
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