Open AccessOn the approximate numerical solutions of fractional heat equation with heat source and heat loss
Author(s) -
Hamı Gündoğdu,
Ömer Faruk Gözükızıl
Publication year - 2022
Publication title -
thermal science/thermal science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.339
H-Index - 43
eISSN - 2334-7163
pISSN - 0354-9836
DOI - 10.2298/tsci210713321g
Subject(s) - laplace transform , fractional calculus , heat equation , mathematics , laplace's equation , exact solutions in general relativity , mittag leffler function , adomian decomposition method , mathematical analysis , partial differential equation
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.