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2013 Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model
Rui Li, Haoqian Zhang, Hao Tao
Abstr. Appl. Anal. 2013(SI42): 1-6 (2013). DOI: 10.1155/2013/615707

Abstract

We study the existence and uniqueness of the positive solution for the fractional differential system involving the Riemann-Stieltjes integral boundary conditions - D t α x ( t ) = f ( t , y ( t ) ) , - D t β y ( t ) = g ( t , x ( t ) ) , t ( 0,1 ) , x ( 0 ) = y ( 0 ) = 0 , x ( 1 ) = 0 1 x ( s ) d A ( s ) , and y ( 1 ) = 0 1 y ( s ) d B ( s ) , where 1 < α , β 2 , and D t α and D t β are the standard Riemann-Liouville derivatives, A and B are functions of bounded variation, and 0 1 D t β x ( s ) d A ( s ) and 0 1 D t β y ( s ) d B ( s ) denote the Riemann-Stieltjes integral. Our results are based on a generalized fixed point theorem for weakly contractive mappings in partially ordered sets.

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Rui Li. Haoqian Zhang. Hao Tao. "Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model." Abstr. Appl. Anal. 2013 (SI42) 1 - 6, 2013. https://doi.org/10.1155/2013/615707

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 07095169
MathSciNet: MR3090294
Digital Object Identifier: 10.1155/2013/615707

Rights: Copyright © 2013 Hindawi

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