摘要
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.
作者
Jiangen LIU
Fazhan GENG
刘建根;耿发展(School of Mathematics and Statistics,Changshu Institute of Technology,Changshu 215500,China;Qin Institute of Mathematics,Shanghai Hanjing Centre for Science and Technology,Shanghai 201609,China)
基金
supported by the NSFC(11971475)
the Natural Science Foundation of Jiangsu Province(BK20230708)
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)。