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Positive solution of nonlinear fractional differential equations with Caputo-like counterpart hyper-Bessel operators. (English) Zbl 1455.34012

In this paper, the author obtain some Grownwall-type integral inequalities involving Mittag-Leffler functions. Using these inequalities and fixed point theorems the author establish the existence and uniqueness of positive solution of initial value problem to nonlinear fractional differential equation with Caputo-like counterpart hyper-Bessel operators.

MSC:

34A08 Fractional ordinary differential equations
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26D07 Inequalities involving other types of functions
33E12 Mittag-Leffler functions and generalizations
47N20 Applications of operator theory to differential and integral equations
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