The Cattaneo type space-time fractional heat conduction equation

The classical heat conduction equation is generalized using a generalized heat conduction law. In particular, we use the space-time Cattaneo heat conduction law that contains the Caputo symmetrized fractional derivative instead of gradient $${{\partial_x}}$$ and fractional time derivative instead of the first order partial time derivative $${{\partial_t}}$$ . The existence of the unique solution to the initial-boundary value problem corresponding to the generalized model is established in the space of distributions. We also obtain explicit form of the solution and compare it numerically with some limiting cases.