ATTRACTIVITY FOR FRACTIONAL EVOLUTION EQUATIONS WITH ALMOST SECTORIAL OPERATORS

In this paper, we initiate the question of the attractivity of solutions for fractional evolution equations with almost sectorial operators. We establish sufficient conditions for the existence of globally attractive solutions for the Cauchy problems in cases that semigroup is compact as well as non-compact. Our results essentially reveal certain characteristics of solutions for fractional evolution equations, which are not possessed by integer order evolution equations.