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Positive solutions of a system of non-autonomous fractional differential equations. (English) Zbl 1064.34004
The paper is about systems of nonautonomous, nonlinear fractional differential equations and the existence of positive solutions. The aim of the paper is to give theorems that provide sufficient conditions for the existence of positive solutions. The basic idea and methodology adopted in the paper is to impose bounds on the (positive) derivatives and to deduce the existence of positive solutions. The analytical tools employed include the Banach and Schauder fixed point theorems.
MSC:
34A34Nonlinear ODE and systems, general
26A33Fractional derivatives and integrals (real functions)
34C99Qualitative theory of solutions of ODE
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)