Fractional view analysis of the diffusion equations via a natural Atangana-Baleanu operator

In this article, the natural transform decomposition method (NTDM) is applied to evaluate the fractional-order diffusion equations utilizing the Atangana-Baleanu operator. The method offers an efficient analytical solution by combining the natural transform methodology with a decomposition strategy. The suggested method incorporates non-local effects and memory qualities introduced by the Atangana-Baleanu operator while demonstrating adaptability and applicability to various fractional-order diffusion equations. In comparison to previous analytical techniques, the NTDM has demonstrated the lowest calculation volume and the highest rate of convergence. The obtained results are presented illustratively by using graphical simulations. The suggested method is therefore easily adaptable to other non-linear issues. The NTDM includes comparative analysis capabilities, practicality, and accurate results for researchers and practitioners. In order to solve fractional-order phenomena, particularly diffusion equations, NTDM is regarded as the best analytical technique.

Automated summary

This article introduces a method that uses the natural transform decomposition method to evaluate fractional-order diffusion equations. The method combines the natural transform methodology with a decomposition strategy, providing an efficient solution with low calculation volume and high convergence rate for various fractional-order diffusion equations.