Existence and Uniqueness of Positive Solutions for a Fractional Switched System

Abstract EN

We discuss the existence and uniqueness of positive solutions for the following fractional switched system: (Dc0+αu(t)+fσ(t)(t,u(t))+gσ(t)(t,u(t))=0, t∈J=[0,1]); (u(0)=u′′(0)=0,u(1)=∫01u(s) ds), where Dc0+α is the Caputo fractional derivative with 2<α≤3, σ(t):J→{1,2,…,N} is a piecewise constant function depending on t, and ℝ+=[0,+∞), fi,gi∈C[J×ℝ+,ℝ+], i=1,2,…,N.

Our results are based on a fixed point theorem of a sum operator and contraction mapping principle.

Furthermore, two examples are also given to illustrate the results.