On the approximate numerical solutions of fractional heat equation with heat source and heat loss

Abstract

In this paper, we are interested in obtaining an approximate numerical solution of the fractional heat equation where the fractional derivative is in Caputo sense. We also consider the heat equation with a heat source and heat loss. The fractional Laplace-Adomian decomposition method is applied to gain the approximate numerical solutions of these equations. We give the graphical representations of the solutions depending on the order of fractional derivatives. Maximum absolute error between the exact solutions and approximate solutions depending on the fractional-order are given. For the last thing, we draw a comparison between our results and found ones in the literature.

Numerical comparisons for solving fractional order integro-differential equations with non-local boundary conditions

“…In the last few decades, fractional calculus became more popular due to its wide range of applications in various fields. Some recent applications of fractional calculus are investigated in the fields of science and engineering such as viscoelasticity [1][2][3], signal processing [4], physics [5,6], bioengineering [7,8], hydrology [9] and biology [10,11]. For the details, the development of fractional calculus can be found in Podlubny [12].…”