Transient fractional heat conduction with generalized Cattaneo model

The generalized Cattaneo equation is a new heat conduction equation which is based on the time-nonlocal generalization of Fourier law. The fractional calculus approach is used in the generalized Cattaneo model. With the help of the Laplace transform, the exact solution of an initial-boundary value problem is obtained and presented under series forms in terms of the H-functions, which is suitable for numerical computation. The solutions of some special cases can also be concluded from the result of this paper. Finally, the influences of the model parameters on the temperature distribution are spotlighted by graphical illustrations.