Attractivity for a k-dimensional system of fractional functional differential equations and global attractivity for a k-dimensional system of nonlinear fractional differential equations

Dumitru Baleanu,Sayyedeh Zahra Nazemi,Shahram Rezapour

doi:10.1186/1029-242x-2014-31

Abstract

In this paper, we present some results for the attractivity of solutions for a k-dimensional system of fractional functional differential equations involving the Caputo fractional derivative by using the classical Schauder’s fixed-point theorem. Also, the global attractivity of solutions for a k-dimensional system of fractional differential equations involving Riemann-Liouville fractional derivative are obtained by using Krasnoselskii’s fixed-point theorem. We give two examples to illustrate our main results.

Highlights

In recent years, many researchers have been focused on investigation of fractional differential equations which has played an important role in different areas of science
In, Chen et al reviewed the global attractivity of solutions for the nonlinear fractional differential equation Dαx(t) = g(t, x(t)) for t ∈ (t, ∞) via the boundary value problem [Dα– x(t)]t=t = x, where t ≥, < α
We investigate the global attractivity of solutions for another k-dimensional system of nonlinear fractional differential equations

Summary

Introduction

Problem x(t ) = x , where t ≥ , < α < , x is a constant, cD is the standard Caputo fractional derivative, and g : (t , ∞) × R → R a function with some properties [ ]. We investigate the attractivity of solutions for a k-dimensional system of fractional differential equations. We investigate the global attractivity of solutions for the k-dimensional system of nonlinear fractional differential equations g (t, x (t), x (t), .

Main results

Conclusions