Sharp extensions and algebraic properties for solution families of vector-valued differential equations (Q258965)

In this paper, the authors prove the property that extension from local to global without loss of regularity holds for the solutions of vector-valued differential equations, in particular for the class of fractional abstract Cauchy problems in the subdiffusive case. The main technique is the use of the algebraic structure of these solutions, which are defined by new versions of functional equations defining solution families of bounded operators. The convolution product and the double Laplace transform for functions of two variables are used to extend these solutions. Finally, different concrete examples are provided to illustrate the results.