Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper...Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.展开更多
T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives....T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.展开更多
In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)...In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.展开更多
文摘Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.
文摘T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.
文摘In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.