Abstract
In this paper we consider a final value problem for a diffusion equation with time-space fractional differentiation on a bounded domain D of Rk<i, k >= 1, which includes the fractional power L beta<i, 0 < beta <= 1, of a symmetric uniformly elliptic operator LL2(D). A representation of solutions is given by using the Laplace transform and the spectrum of L beta<i. We establish some existence and regularity results for our problem in both the linear and nonlinear case.