, Volume 79, Issue 3, pp 507-514
Date: 30 Jun 2009

Existence and uniqueness of mild solutions for semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays

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Abstract

In this paper, we establish the existence and uniqueness of mild solutions for a class of semilinear integro-differential equations of fractional order with nonlocal initial conditions and delays in α-norm. And the main tool is the fixed point theorem due to Sadovskii. Some known results are generalized.

Communicated by Jerome A. Goldstein.
The second author would like to thank the Australian Research Council for funding this project through Discovery Project DP0770388.