Existence of mild solutions for fractional evolution equations with nonlocal initial conditions
Tom 110 / 2014
Annales Polonici Mathematici 110 (2014), 13-24 MSC: Primary 34A08; Secondary 34G20, 35R11, 47D06. DOI: 10.4064/ap110-1-2
This paper discusses the existence of mild solutions for a class of semilinear fractional evolution equations with nonlocal initial conditions in an arbitrary Banach space. We assume that the linear part generates an equicontinuous semigroup, and the nonlinear part satisfies noncompactness measure conditions and appropriate growth conditions. An example to illustrate the applications of the abstract result is also given.