Fractal–fractional operator for COVID-19 (Omicron) variant outbreak with analysis and modeling

The fractal–fraction derivative is an advanced category of fractional derivative. It has several approaches to real-world issues. This work focus on the investigation of 2nd wave of Corona virus in India. We develop a time-fractional order COVID-19 model with effects of disease which consist system of fractional differential equations. Fractional order COVID-19 model is investigated with fractal–fractional technique. Also, the deterministic mathematical model for the Omicron effect is investigated with different fractional parameters. Fractional order system is analyzed qualitatively as well as verify sensitivity analysis. The existence and uniqueness of the fractional-order model are derived using fixed point theory. Also proved the bounded solution for new wave omicron. Solutions are derived to investigate the influence of fractional operator which shows the impact of the disease on society. Simulation has been made to understand the actual behavior of the OMICRON virus. Such kind of analysis will help to understand the behavior of the virus and for control strategies to overcome the disseise in community.