Global existence for semi-linear time fractional σ-evolution equations

Abstract

We investigate the global existence of small data solutions to the Cauchy problem for the semi-linear time fractional σ-evolution equation models with nonlinearity of derivative type and memory. Based on the Lr − Lq estimates obtained in linear problem, and combined with the global iteration method, the global existence of small data solutions is proved under certain conditions of power p. Furthermore, we find that in the low-dimensional case, the limit of our conclusion can match the critical exponent in classical results.