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    A Standardized Numerical Methodology and Analysis for the Time Delayed Fractional Epidemic Model of Infectious Illnesses Spread by Lumpy Skin
    (L and H Scientific Publishing, LLC, 2025-06) Mudassar Rafique; Muhammad Aziz Ur Rehamn; Muhammad Rafiq; Zafar Iqbal; Nauman Ahmed; Ali Akgul
    This study aims to investigate the solution of fractional order delayed lumpy skin infection model with Caputo operator numerically as well as analytically. This delay factor helps to control and slow down the spread of infection in individuals. In this study, existence and uniqueness of the underlying model is discussed. Equilibria of the lumpy skin model are computed along with reproductive number (R0), if R0 > 1 refers spread of illness and if R0 < 1 means control of disease. Local and global stability of fraction delayed model is also presented. Moreover, positive and bounded solution of proposed model are investigated. For the numerical solution of this model, we use Grunwald Letnikov non-standard finite difference scheme. The key properties of the numerical scheme are also investigated like positivity and boundedness. Numerical example is given to present the graphical solution of the fractional order delay epidemic model.