Almost Sectorial Operators in Fractional Superdiffusion Equations.

In this paper the resolvent family { S α , β (t) } t ≥ 0 ⊂ L (X , Y) generated by an almost sectorial operator A, where α , β > 0 , X, Y are complex Banach spaces and its Laplace transform satisfies S ^ α , β (z) = z α - β (z α - A) - 1 is studied. This family of operators allows to write the solution to an abstract initial value problem of time fractional type of order 1 < α < 2 as a variation of constants formula. Estimates of the norm ‖ S α , β (t) ‖ , as well as the continuity and compactness of S α , β (t) , for t > 0 , are shown. Moreover, the Hölder regularity of its solutions is also studied. [ABSTRACT FROM AUTHOR]