Modern Perspectives on Mathematical Modeling: The Power of the Sumudu Transform and Iterative Approaches

Abstract

This work uses the Sumudu transform method to discover approximate analytical solutions for systems of fractional nonlinear equations of population dynamics model and a fractional mathematical model of honey bees. The Caputo sense is used to describe fractional derivatives. In order to get approximate analytical solutions of systems of nonlinear equations of these models, the Sumudu transform method has been developed. Since it provides us with incredibly accurate solutions for both linear and nonlinear differential equations, this approach is simple to understand. It has also been investigated how the power-law kernel via Caputo derivative affects things. To demonstrate the simulations of the answers, we present some figures. © 2026 NSP.