Positive Solutions for a Coupled Nonlinear Fractional Differential System with Coefficients that Change Signs
Zhoujin Cui
Jiangsu Maritime Institute, Jiangsu Nanjing 211100, China.
Zuodong Yang *
School of Teacher Education, Nanjing Normal University, Jiangsu Nanjing 210097, China and Institute of Mathematics, School of Mathematical Science, Nanjing Normal University, Jiangsu Nanjing 210023, China.
*Author to whom correspondence should be addressed.
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.
Keywords: Riemann-Liouville fractional derivatives, Positive solutions, Fixed point theorem in cones.