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Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations

Diethelm, Kai (2007)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10We consider ordinary fractional differential equations with Caputo-type differential operators with smooth right-hand sides. In various places in the literature one can find the statement that such equations cannot have smooth solutions. We prove that this is wrong, and we give a full characterization of the situations where smooth solutions exist. The results can be extended to a class of weakly singular Volterra integral equations.

Solution sets of multivalued Sturm-Liouville problems in Banach spaces

Alessandro Margheri, Pietro Zecca (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We give some results about the topological structure of solution sets of multivalued Sturm-Liouville problems in Banach spaces.

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