Theoretical analysis and computer simulations of a fractional order bank data model incorporating two unequal time delays

In order to reveal the change law of bank data and manage bank effectively, building mathematical models is a very effective approach. In this present study, we set up a novel fractional-order bank data model incorporating two unequal time delays. Firstly, we discuss the existence and uniqueness, non-negativeness, boundedness of the solution to the established bank data model by virtue of contraction mapping theorem, mathematical analysis technique, construct of an appropriate function, respectively. Secondly, the stability and the creation of Hopf bifurcation are investigated via the stability criterion and bifurcation principle of fractional-order differential equation, five new delay-independent stability conditions and bifurcation criteria ensuring the stability behavior and the onset of Hopf bifurcation of the involved bank data model are established. Furthermore, the role of time delay in stabilizing system and controlling the generation of Hopf bifurcation is sufficiently displayed. Thirdly, the global stability of the considered fractional-order bank data model is systematically explored. Fourthly, the Hopf bifurcation control issue of fractional-order bank data model is studied via PD.. controller. Finally, computer simulations are executed to verify the established primary results. The derived conclusions of this study are absolutely innovative and possess important theoretical guiding significance in maintaining a good operation of banks.

Automated summary

In this study, a novel fractional-order bank data model with two unequal time delays is established. The existence, non-negativeness and boundedness of the solution to the model are discussed, and the stability and the creation of Hopf bifurcation are investigated. Five new delay-independent stability conditions and bifurcation criteria are established, ensuring the stability behavior and the onset of Hopf bifurcation in the model. The role of time delay in stabilizing the system and controlling the generation of Hopf bifurcation is also explored. The study provides innovative conclusions and important theoretical guidance for maintaining the proper operation of banks.