Zhang, Kangqun Positive solution of nonlinear fractional differential equations with Caputo-like counterpart hyper-Bessel operators. (English) Zbl 1455.34012 Math. Methods Appl. Sci. 43, No. 6, 2845-2857 (2020). 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. Reviewer: Krishnan Balachandran (Coimbatore) Cited in 4 Documents 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 Keywords:Caputo fractional derivative; Caputo-like counterpart hyper-Bessel operator; fractional differential equation; Gronwall-type integral inequality; positive solution PDFBibTeX XMLCite \textit{K. Zhang}, Math. Methods Appl. Sci. 43, No. 6, 2845--2857 (2020; Zbl 1455.34012) Full Text: DOI