Mathematical Lemon Disease Model via Fractal-Fractional Operators: Analysis Under the Caputo Formulation with Numerical Comparison to Atangana-Baleanu-Caputo and Caputo-Fabrizio

Citrus diseases impose substantial annual losses on global agriculture, threatening both food supply and the economic returns of growers worldwide. In this study, we advance the mathematical understanding of multi-pathogen citrus disease dynamics using fractal-fractional calculus in the Caputo sense. We examine the equilibrium points of the proposed model and establish the existence, uniqueness, and Hyers-Ulam stability of its solutions under the fractal-fractional Caputo (FF Caputo) formulation. We further formulate a numerical scheme based on the generalized Euler method and implement it under three related fractal-fractional operators (FF Caputo, Atangana-Baleanu-Caputo, and Caputo-Fabrizio) to compare their predicted disease dynamics under a range of parameter scenarios. The resulting simulations provide insight into disease progression and inform the design of disease-management strategies. By providing a mathematical basis for the control of plant disease, this work contributes to Sustainable Development Goals 2 (Zero Hunger) and 3 (Good Health and Well-being), supporting sustainable agriculture, plant health, and food security.