TY - JOUR
TI - A new numerical technique for solving fractional sub-diffusion and reaction sub-diffusion equations with a non-linear source term
AU - Bhrawy Ali H
AU - Baleanu Dumitru
AU - Mallawi Fouad Othman M.
JN - Thermal Science
PY - 2015
VL - 19
IS - 11
SP - 25
EP - 34
PT - Article
AB - In this paper, we are concerned with the fractional sub-diffusion equation  with a non-linear source term. The Legendre spectral collocation method is  introduced together with the operational matrix of fractional derivatives  (described in the Caputo sense) to solve the fractional sub-diffusion  equation with a non-linear source term. The main characteristic behind this  approach is that it reduces such problems to those of solving a system of  algebraic equations which greatly simplifying the problem. In addition, the  Legendre spectral collocation methods applied also for a solution of the  fractional reaction sub-diffusion equation with a non-linear source term. For  confirming the validity and accuracy of the numerical scheme proposed, two  numerical examples with their approximate solutions are presented with  comparisons between our numerical results and those obtained by other  methods.