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Sub-diffusion equations with Mittag-Leffler nonlinearity

The paper is devoted to the study of subdiffusion equations with Mittag-Leffler nonlinearity. The comparison principle is proved in a bounded domain. The results on the local existence, global existence, and blow-up of solutions to the initial-boundary value problem are obtained. In addition, the results of local existence and blow-up of solutions to the initial problem on the whole Euclidean space are proven.