Modified Laplace-Adomian Decomposition Method for Solving System of Fractional Partial Differential Equations

Abstract

This study introduces the development and application of Canonical polynomials as a novel alternative to Modified Laplace-Adomian Decomposition Method for solving nonlinear fractional partial differential equations. These polynomials are constructed to simplify complex computations by employing a recursive generation process, thereby reducing the overall computational complexity typically associated with such equations. To evaluate the effectiveness of the proposed approach, a selection of illustrative examples was analyzed. The results demonstrated excellent agreement with solutions reported in the existing literature, underscoring the method's accuracy and reliability. The recursive nature of Canonical polynomials not only enhances computational efficiency but also ensures a systematic and straightforward implementation process, making the method accessible for a wide range of applications. One of the most significant advantages of this approach is its adaptability for programming, as the recursive generation simplifies algorithmic design and execution. This feature makes the method particularly suitable for integration into modern computational tools and software packages. In addition to its computational merits, the proposed method's accuracy and efficiency establish it as a robust alternative for tackling nonlinear fractional partial differential equations. Its simplicity and versatility further contribute to its appeal, providing researchers and practitioners with a practical and reliable tool for addressing challenging problems in the field of fractional calculus. This study demonstrates that Canonical polynomials offer a promising pathway for advancing the solution techniques for nonlinear fractional equations, paving the way for further research and applications.