Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new f...Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.展开更多
本文首先简要回顾了启发式教学法,从苏格拉底的助产术到孔子的温故而知新谈到了现代数学教学模式MM(Methodology of Mathematics)教学法。根据当前教学现状,我们将大学数学教学模式划分为三类形式,即照本宣科模式、小启发模式(简称小启...本文首先简要回顾了启发式教学法,从苏格拉底的助产术到孔子的温故而知新谈到了现代数学教学模式MM(Methodology of Mathematics)教学法。根据当前教学现状,我们将大学数学教学模式划分为三类形式,即照本宣科模式、小启发模式(简称小启发)和大启发模式(简称大启发)。特别地指出了大启发不仅是教学创新模式,也是科研创新的思想方法。为了贯彻大启发教学,最后提出了大学数学教师应有的基本教学素质。展开更多
基金supported by the NSFC(11971475)the Natural Science Foundation of Jiangsu Province(BK20230708)+2 种基金the Natural Science Foundation for the Universities in Jiangsu Province(23KJB110003)Geng's research was supported by the NSFC(11201041)the China Postdoctoral Science Foundation(2019M651765)。
文摘Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.
文摘本文首先简要回顾了启发式教学法,从苏格拉底的助产术到孔子的温故而知新谈到了现代数学教学模式MM(Methodology of Mathematics)教学法。根据当前教学现状,我们将大学数学教学模式划分为三类形式,即照本宣科模式、小启发模式(简称小启发)和大启发模式(简称大启发)。特别地指出了大启发不仅是教学创新模式,也是科研创新的思想方法。为了贯彻大启发教学,最后提出了大学数学教师应有的基本教学素质。
