Tempered Fractional Order Compartment Models And Application

Compartment models have always been a very interesting mathematical model,which have attracted many scholars.Compartment models have important applications in the field of biology and are typically used to model a wide variety of phenomena.At present,there are many literatures on compartment models including fractional derivative,but few literatures on compartment models including tempered fractional order.In this paper we derive the compartment models with tempered fractional derivative by considering the governing equations from underlying stochastic processes.In the stochastic process,we think of the state of the system as the compartment,individuals enter a compartment,waiting for a random time,and then leaving the compartment.The governing equations we derive describe the time evolution of an ensemble of individuals that are undergoing this process.Tempered fractional order compartment models are obtained when the waiting time in a compartment governed by a non-Markovian process following exponential power-law distribution.At the same time,we also ensure that the tempering fractional order model does not violate the laws of physicsIn order to enrich the content of the paper,in the last part of this paper,we listed three examples of compartment models,and for the last example,we carried out numerical simulation.The results show that tempered fractional order differential equation can fit the real data better than the fractional order or integer order differential equation.It shows that the tempered fractional order differential equation is more practical.