In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using ...In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.展开更多
This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-...This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-Stokes equation to find approximate solutions to the problem of lid-driven square cavity flow. The new approach, called PYRDM, considerably improves the convergence rate of the truncated series solution of RDTM and also is based on a simple process that yields highly precise estimates. The numerical results achieved by this method are compared to earlier studies’ results. Our results indicate that this method is more efficient and precise in generating analytic solutions. Furthermore, it provides highly precise solutions with good convergence that is simple to apply for great Reynolds and low Mach numbers. Moreover, the new solution’ graphs demonstrate the new approach’s validity, usefulness, and necessity.展开更多
基金funded by“Taif University Researchers Supporting Project number(TURSP-2020/160),Taif University,Taif,Saudi Arabia”.
文摘In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.
文摘This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-Stokes equation to find approximate solutions to the problem of lid-driven square cavity flow. The new approach, called PYRDM, considerably improves the convergence rate of the truncated series solution of RDTM and also is based on a simple process that yields highly precise estimates. The numerical results achieved by this method are compared to earlier studies’ results. Our results indicate that this method is more efficient and precise in generating analytic solutions. Furthermore, it provides highly precise solutions with good convergence that is simple to apply for great Reynolds and low Mach numbers. Moreover, the new solution’ graphs demonstrate the new approach’s validity, usefulness, and necessity.
