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Title: Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
Authors: Diethelm, Kai
Keywords: Fractional Differential Equation
Initial Value Problem
Caputo Derivative
Weakly Singular Volterra Integral Equation
Issue Date: 2007
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 10, No 2, (2007), 151p-160p
Abstract: We 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.
Description: Mathematics Subject Classification: 26A33, 34A25, 45D05, 45E10
ISSN: 1311-0454
Appears in Collections:2007

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