In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respec...In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the GrunwaldLetnikov method(GLM) and the fractional differential transform method(FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.展开更多
Ca^(2+)signals have a crucial role in the immune system for cell functions such as proliferation,differentiation,apoptosis and gene transcription as well as the activation of Nuclear factor of activated T Cell(NFAT)wh...Ca^(2+)signals have a crucial role in the immune system for cell functions such as proliferation,differentiation,apoptosis and gene transcription as well as the activation of Nuclear factor of activated T Cell(NFAT)which modulates the immune response of the cells.In this study,a fractional order spatiotemporal calcium dynamics model is formulated using the reaction-diffusion equation incorporating parameters like buffers,source influx,Jsscyt and J_(PMCA).Grinwald estimation is employed to obtain the solution and stability analysis has been performed.The analysis of numerical results provides novel insights about the role of Brownian motion,super diffusion,source influx,buffers,etc.,in the regulation of calcium and NFAT concentration levels in T cell and the conditions which might lead to disordered immune responses causing diseases such as HINI,HIV and HBV.展开更多
In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as th...In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function.The Petrov-Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically.The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method(VIM)and exact solutions.For fractional order,the numerical outcomes of fractional Sharma-Tasso-Olver equations are also compared with those obtained by variational iteration method(VIM)in Song et al.[Song L.,Wang Q.,Zhang H.,Rational approximation solution of the fractional Sharma-Tasso-Olver equation,J.Comput.Appl.Math.224:210-218,2009].Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.展开更多
Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a di...Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)models.The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data.In the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)definition.Particle swarm optimization(PSO)algorithm is used to perform data fitting.Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data.An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.展开更多
文摘In this paper, two numerical methods are proposed for solving distributed-order fractional Bagley-Torvik equation.This equation is used in modeling the motion of a rigid plate immersed in a Newtonian fluid with respect to the nonnegative density function. Using the composite Boole's rule the distributedorder Bagley-Torvik equation is approximated by a multi-term time-fractional equation, which is then solved by the GrunwaldLetnikov method(GLM) and the fractional differential transform method(FDTM). Finally, we compared our results with the exact results of some cases and show the excellent agreement between the approximate result and the exact solution.
文摘Ca^(2+)signals have a crucial role in the immune system for cell functions such as proliferation,differentiation,apoptosis and gene transcription as well as the activation of Nuclear factor of activated T Cell(NFAT)which modulates the immune response of the cells.In this study,a fractional order spatiotemporal calcium dynamics model is formulated using the reaction-diffusion equation incorporating parameters like buffers,source influx,Jsscyt and J_(PMCA).Grinwald estimation is employed to obtain the solution and stability analysis has been performed.The analysis of numerical results provides novel insights about the role of Brownian motion,super diffusion,source influx,buffers,etc.,in the regulation of calcium and NFAT concentration levels in T cell and the conditions which might lead to disordered immune responses causing diseases such as HINI,HIV and HBV.
文摘In this paper,time-fractional Sharma-Tasso-Olver(STO)equation has been solved numerically through the Petrov-Galerkin approach utilizing a quintic B-spline function as the test function and a linear hat function as the trial function.The Petrov-Galerkin technique is effectively implemented to the fractional STO equation for acquiring the approximate solution numerically.The numerical outcomes are observed in adequate compatibility with those obtained from variational iteration method(VIM)and exact solutions.For fractional order,the numerical outcomes of fractional Sharma-Tasso-Olver equations are also compared with those obtained by variational iteration method(VIM)in Song et al.[Song L.,Wang Q.,Zhang H.,Rational approximation solution of the fractional Sharma-Tasso-Olver equation,J.Comput.Appl.Math.224:210-218,2009].Numerical experiments exhibit the accuracy and efficiency of the approach in order to solve nonlinear fractional STO equation.
文摘Practical performances of controller design methods strongly depend on relevancy of identified models.Fractional order system models promise advantage of more accurate modeling of real systems.This study presents a discussion on utilization of two fundamental numerical solution methods of fractional calculus in identification problems of One Noninteger Order Plus Time Delay with one pole(NOPTD-I)models.The identification process is carried out by estimating parameters of a NOPTD-I type transfer function template so that the step response of the NOPTD-I model can sufficiently fit experimental step response data.In the study,step responses of NOPTD-I models are numerically calculated according to two fundamental methods,which are Mittag-Leffler(ML)function and Grunwald-Letnikov(GL)definition.Particle swarm optimization(PSO)algorithm is used to perform data fitting.Illustrative examples are presented to evaluate model parameter estimation performances of these two methods for synthetically generated noisy test data.An experimental study is conducted for modeling pitch rotor of TRMS to compare experimental performances.
