Analyzing fractional order variable coefficients heat model

Abstract

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.