This paper deals with the existence of mild solutions for a class of fractional evolution equations with compact analytic semigroup. We prove the existence of mild solutions, assuming that the nonlinear part satisfies some local growth conditions in fractional power spaces. An example is also given to illustrate the applicability of abstract results.
"Existence of Mild Solutions for a Class of Fractional Evolution Equations with Compact Analytic Semigroup." Abstr. Appl. Anal. 2012 (SI01) 1 - 15, 2012. https://doi.org/10.1155/2012/903518