FRACTIONAL ANALYSIS OF POPULATION DYNAMICAL MODEL IN (3+1)-DIMENSIONS WITH FRACTAL-FRACTIONAL DERIVATIVES

The fractal-fractional derivative is a powerful tool that is generally used for the mathematical analysis of complex and unpredictable structures. In this paper, we study a population dynamical model of (3+1)-dimensional form using the fractal derivative involving fractional order with power law kernel. The proposed scheme is known as the Sumudu Homotopy Transform Method ([Formula: see text]HTM), which depends on the association between the Sumudu Transform ([Formula: see text]T) and the Homotopy Perturbation Method (HPM). The convergence of the derived results is verified by comparing the errors in consecutive iterations with the [Formula: see text]HTM results. We display the behavior of the obtained results in three-dimensional shape across the various orders of fractal and fractional derivatives. We present three numerical tests to validate the accuracy of [Formula: see text]HTM and compare the acquired findings to the exact outcomes of the suggested model. This analysis confirms that the [Formula: see text]HTM results align perfectly with the accurate results. As a result, the [Formula: see text]HTM is widely recognized as a leading computational method for obtaining approximate solutions to various nonlinear complex fractal-fractional problems.