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Space-time estimates of linear flow and application to some nonlinear integro-differential equations corresponding to fractional-order time derivative
In this paper we study a class of nonlinear integro-differential equations which correspond to a fractional-order time derivative and interpolate nonlinear heat and wave equations. For this purpose we first establish some space--time estimates of the linear flow which is produced by Mittag--Leffler's functions based on Mihlin--Hörmander's multiplier estimates and …