New Numerical Solutions for Caputo–Fabrizio Fractional Differential Multidimensional Diffusion Problems

This study examined the multidimensional fractional diffusion equations that characterize the density dynamics in a diffusing medium utilizing the exact and analytical Aboodh transform decomposition method (ATDM). The Caputo–Fabrizio (CF) derivative is utilized to account for the fractional derivative that is being employed here. The suggested method handles nonlinear terms by combining the Adomian decomposition method (ADM) with the Aboodh transform (AT) and Adomian polynomials. Since the AT can only be applied to linear equations, ADM is a helpful technique for estimating solutions to nonlinear differential equations. In nonlinear systems, multidimensional diffusion problems which account for the production of stripes in two-dimensional systems are important. Additionally, we used MATLAB to compute numerical and graphical data that illustrate how the close-form analytical solution compares to the precise solution. Promising and appropriate for addressing multidimensional diffusion problems with fractional derivatives are the obtained results. The key benefit is that our devised approach does not depend on presumptions or constraints on variables that skew the actual issue. Overcoming fluctuating constraints that can make it difficult to discover the answer and represent the problem depends much on this technique. In the domains of science and technology, the approach presented in this work offers exceptional computational accuracy and convenience of use for analyzing and resolving intricate phenomena associated with CF fractional nonlinear partial differential equations.