LOCAL FRACTIONAL REDUCED DIFFERENTIAL TRANSFORM METHOD FOR SOLVING
FRACTAL HEAT CONDUCTION EQUATIONS
Abstract
In this study, time-space fractional heat conduction equation (HCEs),
which plays an important role in thermal science, is considered on
Cantor set. The analytical solution of this equation is obtained by
using local fractional reduced differentiable transform method in
fractal spaces. After giving preliminaries, some definitions and
fundamental properties belong to this procedure are given. Then to make
it easy to understand, this method is applied to homogeneous and
non-homogeneous time-space fractional HCEs and analytic solutions are
obtained. After that, physical behaviours of the solutions on fractal
spaces are illustrated in 3D graphics. This shows the efficiency and
reliability of the method.