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2012 Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations
Azizollah Babakhani, Dumitru Baleanu
Abstr. Appl. Anal. 2012(SI01): 1-14 (2012). DOI: 10.1155/2012/632681

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 .

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Azizollah Babakhani. Dumitru Baleanu. "Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations." Abstr. Appl. Anal. 2012 (SI01) 1 - 14, 2012. https://doi.org/10.1155/2012/632681

Information

Published: 2012
First available in Project Euclid: 5 April 2013

zbMATH: 1251.34010
MathSciNet: MR2947672
Digital Object Identifier: 10.1155/2012/632681

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI01 • 2012
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