Existence, Uniqueness, and Stability Analysis of the Fractional-Order Burke-Shaw Model with ABC-Fractional Derivativ

The Burke-Shaw model (BSM), which is grounded in the Lorenz system, is essential in various areas of physics and engineering. In this paper, we investigate the application of a fractional derivative with a Mittag Leffler (M-L) type kernel to address the existence, uniqueness, and Hyers-Ulam stability (HUS) of solutions for the fractional-order BSM. We utilize the ABC-fractional derivative, developed by Atangana and Baleanu, as it offers a more adaptable approach suitable for a diverse array of real-world applications. To demonstrate the existence and uniqueness of solutions, as well as HUS, we introduce a set of necessary conditions that ensure the results presented in this study.