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Positive solutions for coupled nonlinear fractional differential equations. (English) Zbl 1442.34021
Summary: We consider the existence of positive solutions for a coupled system of nonlinear fractional differential equations with integral boundary values. Assume the nonlinear term is superlinear in one equation and sublinear in the other equation. By constructing two cones $$K_1, K_2$$ and computing the fixed point index in product cone $$K_1 \times K_2$$, we obtain that the system has a pair of positive solutions. It is remarkable that it is established on the Cartesian product of two cones, in which the feature of two equations can be opposite.
##### MSC:
 34A08 Fractional ordinary differential equations and fractional differential inclusions 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
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