(untitled) (Journal of Mathematical Modeling and Fractional Calculus, 2024)
One of the most helpful operators for using fractional differential equations to explain non local behaviors is the fractal fractional with Mittage-Leffler kernel fractional derivative. We proposed the fractal fractional Mittage-Leffler kernel for the drinking epidemic which is the world wide largest issue now a days. Qualitative and quantitative analysis for model and scheme are analyzed for drinking system in community. Additionally, using several well-known theorems from fixed point theory, we confirm the existence, uniqueness, analysis, and Ulam-Hyres stability of solutions to a specific class of fractional operators. Connect the drinking fractional system to a recently proposed bivariate Mittag Leffler function to solve it. Some important properties were also verified for Mittage-Leffler fractional derivative on the fractional drinking system. Comparison has been made to the integer order derivative to verify the efficiency of results and effect of drinkers in community.