Abstract and Applied Analysis

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

Azizollah Babakhani and Dumitru Baleanu

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Abstract

We discuss the existence and uniqueness of solution to nonlinear fractional order ordinary differential equations ( D α - ρ t D β ) x ( t ) = f ( t , x ( t ) , D γ x ( t ) ) , t ( 0 , 1 ) with boundary conditions x ( 0 ) = x 0 ,    x ( 1 ) = x 1 or satisfying the initial conditions x ( 0 ) = 0 ,    x ( 0 ) = 1 , where D α 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 .

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 632681, 14 pages.

Dates
First available in Project Euclid: 5 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1365168369

Digital Object Identifier
doi:10.1155/2012/632681

Mathematical Reviews number (MathSciNet)
MR2947672

Zentralblatt MATH identifier
1251.34010

Citation

Babakhani, Azizollah; Baleanu, Dumitru. Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 632681, 14 pages. doi:10.1155/2012/632681. https://projecteuclid.org/euclid.aaa/1365168369


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