Comparative analysis of fractional dynamical systems with various operators

This article implements an efficient analytical technique within three different operators to investigate the solutions of some fractional partial differential equations and their systems. The generalized schemes of the proposed method are derived for every targeted problem under the influence of each fractional derivative operator. The numerical examples of the non-homogeneous fractional Cauchy equation and three-dimensional Navier-Stokes equations are obtained using the new iterative transform method. The obtained results under different fractional derivative operators are found to be identical. The 2D and 3D plots have confirmed the close connection between the exact and obtained results. Moreover, the table shows the higher accuracy of the proposed method. Copyright © 2023 the Author(s), licensee AIMS Press.