This paper proposes a core and spectrum allocation algorithm for elastic optical networks based on multi-core fibers. In this context, the fragmentation and crosstalk mitigation algorithm (FraCA) is proposed. FraCA implements mechanisms to reduce spectral fragmentation and inter-core crosstalk in the network, proving efficient when compared with six other algorithms reported in the literature. The numerical results show that when compared with the most competitive of the six algorithms, FraCA achieves a gain of request blocking probability of at least 16.87%, a gain of bandwidth blocking probability of at least 43.95%, and a mean increase in spectral utilization of at least 4.36%.