(untitled) (Journal of Mathematical Modeling and Fractional Calculus, 2024)
The Constant proportional Caputo (CPC) fractional derivative has been one of the most use ful operators for modeling non-local behaviors by fractional differential equations. We proposed the CPC operator for the drinking epidemic which is the world wide largest issue nowadays. In compar ison to the integer-order models, the fractional order differential equations models appear to be more compatible with this illness. Qualitative and quantitative analysis for model and scheme are treated. We also present the uniqueness and Ulam-Hyres stability of solutions to a particular class of fractional starting value issues involving the Hilfer proportional fractional derivative using certain well-known theorems from the fixed point theory. The bivariate Mittag-Leffler function that was recently pub lished will be used to solve the drinking pandemic model, we first construct the inverse operator and Laplace transform of the new formulation also eigenfunctions for the proposed scheme. Some impor tant properties were also verified for the Constant proportional Caputo (CPC) fractional derivative on the epidermic model.