Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an importa...Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.展开更多
In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the ...In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed.Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models.We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.展开更多
文摘Diabetes is a burning issue in the whole world.It is the imbalance between body glucose and insulin.The study of this imbalance is very much needed from a research point of view.For this reason,Bergman gave an important model named-Bergman minimalmodel.In the present work,using Caputo-Fabrizio(CF)fractional derivative,we generalize Bergman’s minimal blood glucose-insulin model.Further,we modify the old model by including one more component known as diet D(t),which is also essential for the blood glucose model.We solve the modified modelwith the help of Sumudu transformand fixed-point iteration procedures.Also,using the fixed point theorem,we examine the existence and uniqueness of the results along with their numerical and graphical representation.Furthermore,the comparison between the values of parameters obtained by calculating different values of t with experimental data is also studied.Finally,we draw the graphs of G(t),X(t),I(t),andD(t)for different values ofτ.It is also clear from the obtained results and their graphical representation that the obtained results of modified Bergman’s minimal model are better than Bergman’s model.
基金This research is supported by the Scientific and Technological Research Council of Turkey(TUBTAK)under the Grant No.TBAG-117F473.
文摘In this paper,we have proposed the efficient numerical methods to solve a tumor-obesity model which involves two types of the fractional operators namely Caputo and CaputoFabrizio(CF).Stability and convergence of the proposed schemes using Caputo and CF fractional operators are analyzed.Numerical simulations are carried out to investigate the effect of low and high caloric diet on tumor dynamics of the generalized models.We perform the numerical simulations of the tumor-obesity model for different fractional order by varying immune response rate to compare the dynamics of the Caputo and CF fractional operators.
