We firstly prove that -times integrated -resolvent operator function (-ROF) satisfies a functional equation which extends that of -times integrated semigroup and -resolvent operator function. Secondly, for the inhomogeneous -Cauchy problem , , , if is the generator of an -ROF, we give the relation between the function and mild solution and classical solution of it. Finally, for the problem , , , where is a linear closed operator. We show that generates an exponentially bounded -ROF on a Banach space if and only if the problem has a unique exponentially bounded classical solution and Our results extend and generalize some related results in the literature.
"Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/430418