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

Abstract

AbstractNowadays, 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.