The Self-similar Solution to Some Nonlinear Integro-differential Equations Corresponding to Fractional Order Time Derivative

In this paper we study the self.similar solution to a class of nonlinear integro.differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space.time estimates which were established by Hirata and Miao in [11] we prove the global existence of self.similar solution of Cauchy problem for the nonlinear integro-differential equation in C.([0,.);B.spp,.(Rn)).