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A Cauchy-type problem with a sequential fractional derivative in the space of continuous functions. (English) Zbl 1279.26016
Summary: A Cauchy-type nonlinear problem for a class of fractional differential equations with sequential derivatives is considered in the space of weighted continuous functions. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. An existence and uniqueness result of the global continuous solution is proved.

MSC:
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations and fractional differential inclusions
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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