![](/images/graphics-bg.png)
Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions
Joint Authors
Source
International Journal of Differential Equations
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-12-10
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
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.
However, ordinary Langevin equation does not provide the correct description of the dynamics for systems in complex media.
In order to overcome this problem and describe dynamical processes in a fractal medium, numerous generalizations of Langevin equation have been proposed.
One such generalization replaces the ordinary derivative by a fractional derivative in the Langevin equation.
This gives rise to the fractional Langevin equation with a single index.
Recently, a new type of Langevin equation with two different fractional orders has been introduced which provides a more flexible model for fractal processes as compared with the usual one characterized by a single index.
The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions of the problem in a Banach space.
American Psychological Association (APA)
Ahmad, Bashir& Nieto, Juan Jose. 2009. Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions. International Journal of Differential Equations،Vol. 2010, no. 2010, pp.1-10.
https://search.emarefa.net/detail/BIM-488136
Modern Language Association (MLA)
Ahmad, Bashir& Nieto, Juan Jose. Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions. International Journal of Differential Equations No. 2010 (2010), pp.1-10.
https://search.emarefa.net/detail/BIM-488136
American Medical Association (AMA)
Ahmad, Bashir& Nieto, Juan Jose. Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions. International Journal of Differential Equations. 2009. Vol. 2010, no. 2010, pp.1-10.
https://search.emarefa.net/detail/BIM-488136
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-488136