Numerical investigations on COVID-19 model through singular and non-singular fractional operators

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 β.