Fractional Differential Equation Initial Value Problem Caputo Derivative Smoothness Weakly Singular Volterra Integral Equation 26A33 34A25 45D05 45E10
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.
