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Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited [PDF]

open access: yesMathematics, 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
doaj   +4 more sources

On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation [PDF]

open access: yesAdvances 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
doaj   +4 more sources

q-Fractional Langevin Differential Equation with q-Fractional Integral Conditions

open access: yesMathematics, 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
doaj   +2 more sources

Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions [PDF]

open access: yesInternational 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
doaj   +2 more sources

Stability of a Nonlinear ML-Nonsingular Kernel Fractional Langevin System with Distributed Lags and Integral Control

open access: yesAxioms, 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
doaj   +2 more sources

Existence, Stability and Simulation of a Class of Nonlinear Fractional Langevin Equations Involving Nonsingular Mittag–Leffler Kernel

open access: yesFractal 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
doaj   +2 more sources

On fractional Langevin equation involving two fractional orders in different intervals

open access: yesNonlinear 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
doaj   +5 more sources

Existence of solution for fractional Langevin equation: Variational approach [PDF]

open access: yesElectronic 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
doaj   +2 more sources

On a Nonlinear Fractional Langevin Equation of Two Fractional Orders with a Multiplicative Noise

open access: yesFractal 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
exaly   +2 more sources

Existence of Solutions to Nonlinear Langevin Equation Involving Two Fractional Orders with Boundary Value Conditions [PDF]

open access: yesBoundary 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
doaj   +2 more sources

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