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Bounds on the solution of a Cauchy-type problem involving a weighted sequential fractional derivative. (English) Zbl 1312.34014
Summary: We establish some bounds for the solution of a Cauchytype problem for a class of fractional differential equations with a weighted sequential fractional derivative. The bounds are based on a Bihari-type inequality and a bound on the Gauss hypergeometric function.

MSC:
34A08 Fractional ordinary differential equations and fractional differential inclusions
33C05 Classical hypergeometric functions, \({}_2F_1\)
45J05 Integro-ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
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