TIME FRACTIONAL LINEAR PROBLEMS ON L² ( R^d )

Hassan Emamirad (1) , Arnaud Rougirel (2)

1 UP - Université de Poitiers = University of Poitiers
2 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]

In this paper, we propose a theory for linear time fractional PDEs on L² ( R^d ). The order of the time derivatives under consideration is less than 1. We study well-posedness, regularizing effects and dissipative properties. In particular, we give a necessary and sufficient condition for well-posedness. Regarding regularizing effects, we describe quite precisely the equations that have this effect or not. We highlight that, in purely fractional settings, the regularizing effect acts always only up to finite order; unlike to the standard case.

Mots clés: Fractional derivatives; Time fractional PDEs; regularizing effect; dissipative inequalities; Fractional Schrödinger equation; Fractional transport equation.

Domaines: Equations aux dérivées partielles [math.AP]

Hassan Emamirad, Arnaud Rougirel. TIME FRACTIONAL LINEAR PROBLEMS ON L² ( R^d ). 2017. ⟨hal-01492949⟩