Abstract

The long memory effects of a system can be regarded as fractional. This paper deals with a newly constructed system of equation for Hepatitis B disease of fractional control problems in sense of Caputo fractional order derivative. The model considers four different health classes of populations, susceptible, acute infections, chronic infections and recovered, as well as a control by applying a strategy of isolation, treatment and vaccination. Initially, the equilibrium points and stability of the system are studied and sensitivity analysis complemented by simulation is performed to determine how changes in parameters affects the dynamical behavior of the system. For singular kernel of fractional derivative, the necessary conditions for optimality of Hepatitis B system are derived. An effective numerical simulation depended on trapezoidal approximation is to verify the control effect in terms of the transient response compared to the different fractional- and integer-order derivatives, and additional graphical solutions are presented for ease of understanding. This study may provide a strong theoretical basis for uncovering the importance of the long memory effects in the control of hepatitis B.