The Cattaneo type space-time fractional heat conduction equation
The classical heat conduction equation is generalized using a generalized heat conduction law. The authors 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. The explicit form of the solution is obtained and numerically compared with some limiting cases.
scientific article; zbMATH DE number 6140918
scientific article