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A Cauchy-type problem involving a weighted sequential derivative in the space of integrable functions. (English) Zbl 1348.34011
Summary: A Cauchy-type nonlinear problem for a class of fractional differential equations involving sequential derivatives is considered. Some properties and composition identities are derived. The equivalence with the associated integral equation is established. The existence and uniqueness of global solutions in the space of Lebesgue integrable functions are proved.

34A08 Fractional ordinary differential equations and fractional differential inclusions
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
Full Text: DOI
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