TY - JOUR
TI - Analyzing fractional order variable coefficients heat model
AU - Elamin Mawahib
AU - Helalb Khadeeja A
AU - Abdel-Khalek Sayed
AU - Mubaraki Ali M
AU - Albogami Tahani M
AU - Abdel-Salam Emad A.-B
JN - Thermal Science
PY - 2024
VL - 28
IS - 6
SP - 5143
EP - 5152
PT - Article
AB - The manuscript's primary goal is to utilize the decomposition Adomian  approach to approximate solutions for a specific class of space-time  fractional order heat model characterized by variable coefficients and  appropriate initial values. This method allows for the computation of a  power series representation of the solution without the need for  linearization, assumptions about weak non-linearity, or reliance on  perturbation theory. By employing mathematical software like MATHEMATICA or  Maple, the Adomian formulas are employed to evaluate the resulting series  solution. Furthermore, this approach shows promise in addressing various  types of fractional order non-linear mathematical physics models. The  analysis reveals a remarkable convergence between the outcomes derived from  the decomposition method utilizing infinite series and the well-established  results obtained when the fractional order equals one. This convergence  underscores the efficacy and accuracy of the decomposition method in  approximating solutions for fractional order equations, particularly when  the fractional order approaches unity. Such alignment between the  decomposition method's results and those derived from conventional  approaches bolsters confidence in its utility and reliability, further  solidifying its standing as a valuable tool in the realm of fractional  calculus and applied mathematics. Notably, the obtained results reveal that  the solution's profile changes based on varying fractional orders. This  indicates that the shape of the solution wave can be altered without  introducing additional parameters. These findings have far-reaching  implications across numerous applications within specific contexts,  suggesting the potential for significant advancements in understanding and  addressing complex physical phenomena governed by fractional order  equations.