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

Abstract EN

We study the existence and uniqueness of the positive solution for the fractional differential system involving the Riemann-Stieltjes integral boundary conditions -Dtαx(t)=f(t,y(t)), - Dtβy(t)=g(t,x(t)), t∈(0,1), x(0)=y(0)=0, x(1)=∫01x(s)dA(s), and y(1)=∫01y(s)dB(s), where 1<α, β≤2, and Dtα and Dtβ are the standard Riemann-Liouville derivatives, A and B are functions of bounded variation, and ∫01Dtβx(s)dA(s) and ∫01Dtβy(s)dB(s) denote the Riemann-Stieltjes integral.

Our results are based on a generalized fixed point theorem for weakly contractive mappings in partially ordered sets.