Abstract and Applied Analysis

Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model

Rui Li, Haoqian Zhang, and Hao Tao

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 615707, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393443521

Digital Object Identifier
doi:10.1155/2013/615707

Mathematical Reviews number (MathSciNet)
MR3090294

Citation

Li, Rui; Zhang, Haoqian; Tao, Hao. Unique Solution of a Coupled Fractional Differential System Involving Integral Boundary Conditions from Economic Model. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 615707, 6 pages. doi:10.1155/2013/615707. https://projecteuclid.org/euclid.aaa/1393443521


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