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Abstract differential equations and Caputo fractional derivative

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Abstract

In this work we consider the abstract Cauchy problem with Caputo fractional time derivative of order \(\alpha \in (0,1]\), and discuss the continuity of the respective solutions regarding the parameter \(\alpha \). We also present a study about the continuity of the Mittag-Leffler families of operators (for \(\alpha \in (0,1]\)), when they are induced by sectorial operators.

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Correspondence to P. M. Carvalho-Neto.

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Communicated by Abdelaziz Rhandi.

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Carvalho-Neto, P.M. Abstract differential equations and Caputo fractional derivative. Semigroup Forum 104, 561–583 (2022). https://doi.org/10.1007/s00233-022-10272-8

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  • DOI: https://doi.org/10.1007/s00233-022-10272-8

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