Opuscula Math. 36, no. 1 (2016), 123-137
http://dx.doi.org/10.7494/OpMath.2016.36.1.123

Opuscula Mathematica

# Fractional evolution equation nonlocal problems with noncompact semigroups

Xuping Zhang
Pengyu Chen

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.

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• Xuping Zhang
• Northwest Normal University, Department of Mathematics, Lanzhou 730 070, P.R. China
• Zhixing College of Northwest Normal University, Department of Mathematics, Lanzhou 730 070, P.R. China
• Pengyu Chen
• Northwest Normal University, Department of Mathematics, Lanzhou 730 070, P.R. China
• Communicated by Alexander Gomilko.
• Revised: 2015-04-23.
• Accepted: 2015-05-07.
• Published online: 2015-09-19.