Geodesic
Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations
Fractional calculus and applied analysis, Tome 10 (2007) no. 2, pp. 151-160.

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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.
Keywords: Fractional Differential Equation, Initial Value Problem, Caputo Derivative, Smoothness, Weakly Singular Volterra Integral Equation, 26A33, 34A25, 45D05, 45E10 
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     author = {Diethelm, Kai},
     title = {Smoothness {Properties} of {Solutions} of {Caputo-Type} {Fractional} {Differential} {Equations}},
     journal = {Fractional calculus and applied analysis},
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     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2007_10_2_a4/}
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Diethelm, Kai. Smoothness Properties of Solutions of Caputo-Type Fractional Differential Equations. Fractional calculus and applied analysis, Tome 10 (2007) no. 2, pp. 151-160. http://geodesic.mathdoc.fr/item/FCAA_2007_10_2_a4/