A Note on Fractional Evolutionary Equations

Abstract

A class of linear evolutionary equations with material laws involving fractional time-derivatives is considered. The main result is well-posedness and causality for this problem class. The approach is illustrated with two examples: a fractional Fokker-Planck type equation and a class of visco-elastic materials described via fractional derivatives. In conclusion the possibility of imposing initial conditions is discussed.

correction to footnote replacing -αby αin some places Paper has been withdrawn due to a crucial error in the positivity estimates