In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued frac...In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.展开更多
为了提高光伏电池转换效率、降低能量损失,有必要研究最大功率点跟踪(maximum power point tracking,MPPT)方法。针对传统扰动观察法(perturbation observation method,P&O)存在无法兼顾跟踪速度与稳态精度、在光照度发生较大变化...为了提高光伏电池转换效率、降低能量损失,有必要研究最大功率点跟踪(maximum power point tracking,MPPT)方法。针对传统扰动观察法(perturbation observation method,P&O)存在无法兼顾跟踪速度与稳态精度、在光照度发生较大变化时会产生误判现象的问题,文中提出一种能适应环境变化的变步长P&O控制策略。首先,利用光伏电池刚启动时类似恒流源的特性获取当前光照度下的短路电流,通过固定电流法推导出最大功率点(maximum power point,MPP)的参考电压;其次,当光照度突变时,提出功率修正方法,并给出突变时的变步长调整策略;最后,设计基于线性扩张状态观测器(linear extended state observer,LESO)的分数阶比例积分微分(fractional order proportion integration differentiation,FOPID)控制器,可以对算法输出的参考电压进一步进行跟踪补偿。仿真结果表明,所提控制策略可以提高稳态精度和跟踪速度,有效提高光伏电池的输出功率。展开更多
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
基金Supported by the National Natural Science Foundation of China(Grant No.11571071)the Natural Science Key Foundation of Education Department of Anhui Province(Grant No.KJ2013A183)+1 种基金the Project of Leading Talent Introduction and Cultivation in Colleges and Universities of Education Department of Anhui Province(Grant No.gxfxZD2016270)the Incubation Project of the National Scientific Research Foundation of Bengbu University(Grant No.2018GJPY04)
文摘In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.
文摘为了提高光伏电池转换效率、降低能量损失,有必要研究最大功率点跟踪(maximum power point tracking,MPPT)方法。针对传统扰动观察法(perturbation observation method,P&O)存在无法兼顾跟踪速度与稳态精度、在光照度发生较大变化时会产生误判现象的问题,文中提出一种能适应环境变化的变步长P&O控制策略。首先,利用光伏电池刚启动时类似恒流源的特性获取当前光照度下的短路电流,通过固定电流法推导出最大功率点(maximum power point,MPP)的参考电压;其次,当光照度突变时,提出功率修正方法,并给出突变时的变步长调整策略;最后,设计基于线性扩张状态观测器(linear extended state observer,LESO)的分数阶比例积分微分(fractional order proportion integration differentiation,FOPID)控制器,可以对算法输出的参考电压进一步进行跟踪补偿。仿真结果表明,所提控制策略可以提高稳态精度和跟踪速度,有效提高光伏电池的输出功率。
