Abstract Nowadays, the complete world is suffering from untreated infectious epidemic disease COVID-19 due to coronavirus, which is a very dangerous and deadly viral infection So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID-19) outbreak through fractional derivatives The adoption of modified mathematical techniques and some basic explanation in this research field will have a strong effect on progressive society fitness by controlling some diseases The main objective of this work is to investigate the dynamics and numerical approximations for the recommended arbitrary-order coronavirus disease system This system illustrating the probability of spread within a given general population In this work, we considered a system of a novel COVID-19 with the three various arbitrary-order derivative operators: Caputo derivative having the power law, Caputo?Fabrizio derivative having exponential decay law and Atangana?Baleanu-derivative with generalized Mittag?Leffler function The existence and uniqueness of the arbitrary-order system is investigated through fixed-point theory We investigate the numerical solutions of the non-linear arbitrary-order COVID-19 system with three various numerical techniques For study, the impact of arbitrary-order on the behavior of dynamics the numerical simulation is presented for distinct values of the arbitrary power ?
Numerical investigations on COVID-19 model through singular and non-singular fractional operators