Opuscula Math. 36, no. 1 (), 123-137
http://dx.doi.org/10.7494/OpMath.2016.36.1.123
Opuscula Mathematica

# Fractional evolution equation nonlocal problems with noncompact semigroups

Abstract. This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.
Keywords: fractional evolution equation, mild solution, nonlocal condition, $$C_0$$-semigroup, condensing maps, measure of noncompactness.
Mathematics Subject Classification: 34A12, 35F25, 35R11.