Results 1 to 10 of about 9,426 (207)
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
doaj +3 more sources
Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited
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
doaj +3 more sources
Fractional Langevin Equations with Nonseparated Integral Boundary Conditions [PDF]
Advances in Mathematical Physics, 2020 In this paper, we discuss the existence of solutions for nonlinear fractional Langevin equations with nonseparated type integral boundary conditions. The Banach fixed point theorem and Krasnoselskii fixed point theorem are applied to establish the results. Some examples are provided for the illustration of the main work.
Khalid Hilal +3 more
openaire +3 more sources
On the new fractional configurations of integro-differential Langevin boundary value problems
Alexandria Engineering Journal, 2021 In this paper, we present the existence criteria for the solutions of boundary value problems involving generalized fractional integro-Langevin equation and inclusion supplemented with nonlocal fractional boundary conditions. The main idea of the current
Shahram Rezapour +2 more
doaj +1 more source
Critical Exponent of the Fractional Langevin Equation [PDF]
Physical Review Letters, 2008 We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase.
S, Burov, E, Barkai
openaire +2 more sources
SOLVABILITY FOR IMPULSIVE FRACTIONAL LANGEVIN EQUATION
Journal of Applied Analysis & Computation, 2020 Summary: We investigate impulsive fractional Langevin equation involving two fractional Caputo derivatives with boundary value conditions. By Banach contraction mapping principle and Krasnoselskii's fixed point theorem, some results on the existence and uniqueness of solution are obtained.
Xu, Mengrui, Sun, Shurong, Han, Zhenlai
openaire +1 more source
Boundary Value Problems, 2023 This research inscription gets to grips with two novel varieties of boundary value problems. One of them is a hybrid Langevin fractional differential equation, whilst the other is a coupled system of hybrid Langevin differential equation encapsuling a ...
A. Boutiara +3 more
doaj +1 more source
Fractional Langevin Equation to Describe Anomalous Diffusion [PDF]
Progress of Theoretical Physics Supplement, 2000 A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger.
Kobelev, V., Romanov, E.
openaire +2 more sources
Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces [PDF]
, 2010 We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights.
B. I. Henry +7 more
core +3 more sources
Controllability of Hilfer fractional Langevin evolution equations
Frontiers in Applied Mathematics and Statistics, 2023 The existence of fractional evolution equations has attracted a growing interest in recent years. The mild solution of fractional evolution equations constructed by a probability density function was first introduced by El-Borai. Inspired by El-Borai, Zhou and Jiao gave a definition of mild solution for fractional evolution equations with Caputo ...
Haihua Wang, Junhua Ku
openaire +2 more sources