Existence results for a generalization of the time-fractional diffusion equation with variable coefficients.

In this paper we consider the Cauchy problem of a generalization of time-fractional diffusion equation with variable coefficients in R+n+1, where the time derivative is replaced by a regularized hyper-Bessel operator. The explicit solution of the inhomogeneous linear equation for any n∈Z+ and its uniqueness in a weighted Sobolev space are established. The key tools are Mittag-Leffler functions, M-Wright functions and Mikhlin multiplier theorem. At last, we obtain the existence of solution of the semilinear equation for n=1 by using a fixed point theorem. [ABSTRACT FROM AUTHOR]