Abstract and Applied Analysis

Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions

Josefa Caballero, Mohamed Abdalla Darwish, Kishin Sadarangani, and Wafa M. Shammakh

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Abstract

We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D 0 + α [ x ( t ) / f ( t , x ( t ) , y ( t ) ) ] = g ( t , x ( t ) , y ( t ) ) , D 0 + α y ( t ) / f ( t , y ( t ) , x ( t ) ) = g ( t , y ( t ) , x ( t ) ) ,     0 < t < 1 , and x ( 0 ) = y ( 0 ) = 0 , where α ( 0,1 ) and D 0 + α denotes the Riemann-Liouville fractional derivative. The main tools in our study are the techniques associated to measures of noncompactness in the Banach algebras and a fixed point theorem of Darbo type.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 672167, 10 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277111

Digital Object Identifier
doi:10.1155/2014/672167

Mathematical Reviews number (MathSciNet)
MR3240553

Zentralblatt MATH identifier
07022848

Citation

Caballero, Josefa; Darwish, Mohamed Abdalla; Sadarangani, Kishin; Shammakh, Wafa M. Existence Results for a Coupled System of Nonlinear Fractional Hybrid Differential Equations with Homogeneous Boundary Conditions. Abstr. Appl. Anal. 2014 (2014), Article ID 672167, 10 pages. doi:10.1155/2014/672167. https://projecteuclid.org/euclid.aaa/1412277111


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