Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations

Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations

We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0,  x(1)=x1 or satisfying the initial conditions x(0)=0,  x′(0)=1, where Dα denotes Caputo fractional derivative, ρ...

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Main Authors: Azizollah Babakhani, Dumitru Baleanu
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/632681
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spelling doaj-e7606141346b4f7d8d841d03e098f56c2020-11-24T22:35:16ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/632681632681Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential EquationsAzizollah Babakhani0Dumitru Baleanu1Department of Mathematics, Faculty of Basic Science, Babol University of Technology, Babol 47148-71167, IranDepartment of Mathematics and Computer Science, Cankaya University, TurkeyWe discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0,  x(1)=x1 or satisfying the initial conditions x(0)=0,  x′(0)=1, where Dα denotes Caputo fractional derivative, ρ is constant, 1<α<2, and 0<β+γ≤α. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f.http://dx.doi.org/10.1155/2012/632681
collection DOAJ
language English
format Article
sources DOAJ
author Azizollah Babakhani
Dumitru Baleanu
spellingShingle Azizollah Babakhani
Dumitru Baleanu
Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
Abstract and Applied Analysis
author_facet Azizollah Babakhani
Dumitru Baleanu
author_sort Azizollah Babakhani
title Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
title_short Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
title_full Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
title_fullStr Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
title_full_unstemmed Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
title_sort existence and uniqueness of solution for a class of nonlinear fractional order differential equations
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations (Dα-ρtDβ)x(t)=f(t,x(t),Dγx(t)), t∈(0,1) with boundary conditions x(0)=x0,  x(1)=x1 or satisfying the initial conditions x(0)=0,  x′(0)=1, where Dα denotes Caputo fractional derivative, ρ is constant, 1<α<2, and 0<β+γ≤α. Schauder's fixed-point theorem was used to establish the existence of the solution. Banach contraction principle was used to show the uniqueness of the solution under certain conditions on f.
url http://dx.doi.org/10.1155/2012/632681
work_keys_str_mv AT azizollahbabakhani existenceanduniquenessofsolutionforaclassofnonlinearfractionalorderdifferentialequations
AT dumitrubaleanu existenceanduniquenessofsolutionforaclassofnonlinearfractionalorderdifferentialequations
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