Positive Solutions for a Coupled Nonlinear Fractional Differential System with Coefficients that Change Signs

Abstract

This paper investigates the existence of positive solutions of the nonlinear fractional di_erential system _   where 0 < s; p < 1, Ds;Dp are the standard Riemann-Liouville fractional derivatives, λ; μ > 0 are parameters. The peculiarity of this coupled equations is the coe_cient functions a(t) and b(t) change signs, unlike the works in the literature keeping the signs of a(t); b(t) unchanged. On the basis of a nonlinear alternative of Leray-Schauder type and Krasnoselskii0s in a cone, suficient conditions on a(t); b(t) guarantee the existence of positive solution of the coupled equations are obtained. The results are illustrated with an example.