首页|AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

AN EXPLANATION ON FOUR NEW DEFINITIONS OF FRACTIONAL OPERATORS

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Fractional calculus has drawn more attentions of mathematicians and engineer-s 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 Caputo-Fabrizio 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 con-nection 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.

k-Prabhakar fractional operatorCaputo-Fabrizio operatorAtangana-Baleanu operatorSun-Hao-Zhang-Baleanu operatorgeneralized Caputo type operator

刘建根、耿发展

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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

NSFCNatural Science Foundation of Jiangsu ProvinceNatural Science Foundation for the Universities in Jiangsu ProvinceNSFCChina Postdoctoral Science Foundation

11971475BK2023070823KJB110003112010412019M651765

2024

10.1007/s10473-024-0405-7

数学物理学报(英文版)
中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD
影响因子：0.256
ISSN：0252-9602
年,卷(期)：2024.44(4)
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