Mathematical insights into fractal-fractional model of Tomato Yellow Leaf Curl disease

In this study, we aim to propose a new model for the tomato yellow curl leaf virus, which involves a fractal-fractional derivative governed by a power law kernel. This novel approach to fractal differentiation combines the concepts of fractional differentiation and fractal derivative, which involves scaling the variable according to tβ, where the recovery of classical derivatives occurs as the fractal order β approaches 1. The dynamical system of equations for the process of the fractional Tomato Yellow Leaf Curl (TYLC) virus model is examined qualitatively and quantitatively in this article. This paper investigates the existence and uniqueness of the system using Banach and fixed point theorems and applies the Ulam–Hyers method for stability analysis. Additionally, numerical simulations of the model are performed using the two-step Lagrange method for approximate solutions.