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Since 2012, the Middle East has seen a steady rise in the Middle East Respiratory Syndrome Coronavirus (MERS-CoV). A fractional derivative of the non-singular Mittag-Leffler type is used in this research to conduct a mathematical analysis of the dynamics of MERS-CoV infection transmission. The dynamics of such a disease with an additional degree of freedom and non-singular behavior are discovered through the use of the aforementioned fractional operator, and this is one of the important components of our prepared paper. Using the concept of fixed point theory, the existence and uniqueness of solutions are demonstrated. The stability analysis is also tested with the help of the Ulam–Hyers approach, respectively. The numerical solution has been conducted by using the fractional Adams–Bashforth scheme. In the numerical simulation, all classes are demonstrated through the graphical presentation regarding the changing values of fractional-order at time t. The results at various fractional-order laying between (0,1] are drawn with the help of Matlab. We also provide a comparison of the proposed approach with that of the Caputo operator. The outcomes that were achieved illustrate that the considered scheme is highly methodical and very efficient compared to the Caputo fractional operator. • The dynamics of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) into fractional derivative is studied in the sense of non-singular kernels. • The considered problem is analyzed for existence and uniqueness of solution with fractional derivative. • The approximate solution of the proposed problem is obtained by the numerical iterative technique of Adams–Bashforth. • Comparison between the proposed scheme and the Caputo operator is also provided. • The outcomes illustrate that the considered scheme is highly methodical and very efficient compared to the Caputo fractional operator. [ABSTRACT FROM AUTHOR]