The Iterative Positive Solution for a System of Fractional q-Difference Equations with Four-Point Boundary Conditions

Abstract

In this work, we investigate the following system of fractional q-difference equations with four-point boundary problems: Dqαut+ft,vt=0,0<t<1;Dqβvt+gt,ut=0,0<t<1;u0=0,u1=γ1uη1; and v0=0,v1=γ2uη2, where Dqα and Dqβ are the fractional Riemann–Liouville q-derivative of order α and β, respectively, 0<q<1, 1<β≤α≤2, 0<η1,η2<1, 0<γ1η1α−1<1, and 0<γ2η2β−1<1. By virtue of monotone iterative approach, the iterative positive solutions are obtained. An example to illustrate our result is given.