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Innovative techniques to chaotic dynamics and kinetic differ-integral equations
(Taylor & Francis Inc, 2025) Mehmood, Ahsan; Liu, Zhi-Guo; Samraiz, Muhammad; Usta, Fuat; Arjika, Sama
In this work, we analyse advancements in chaotic modelling by applying a modified version of the Atangana-Baleanu Caputo (MABC) fractional derivative operator (FDO) with respect to another function within a mathematical model (MMd). We employ an iterative method and fixed-point theory to verify the existence of a unique solution for this model. Additionally, due to the high non-linearity of the problem, we apply an appropriate numerical scheme to solve this system of equations computationally. Graphical representations illustrate the convergence of solutions within the chaotic model. To test the versatility of the modified Atangana-Baleanu Riemann (MABR) FDO, we generalize a kinetic differ-integral equation and compute its solution. The main contribution of our research is the construction of a chaotic model with the MABC FDO and a non-local, nonlinear kernel. Utilizing advanced numerical methods, we transform the non-local kernel into its local counterpart in order to obtain efficient and accurate solutions.