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Existence and uniqueness of positive solutions of a class of nonlinear differential equations of fractional order. (Chinese. English summary) Zbl 1249.34008

Summary: By using a fixed point theorem and the contraction mapping principle on a cone in a real Banach space, the existence and uniqueness of positive solutions of nonlinear fractional differential equations in which the inhomogeneous term depends on the fractional derivative of lower orders are investigated respectively. Based on the expression of the solutions, sufficient conditions for the existence of positive solutions for this type of equations are obtained, also for the uniqueness. Finally, two examples are presented to demonstrate the main results.

MSC:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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