On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems  

作　　者：Muhammad Samraiz Muhammad Umer Thabet Abdeljawad Saima Naheed Gauhar Rahman Kamal Shah 

机构地区：[1]Department of Mathematics,University of Sargodha,P.O.Box 40100,Sargodha,40100,Pakistan [2]Department of Mathematics and Sciences,Prince Sultan University,P.O.Box 66833,Riyadh,11586,Saudi Arabia [3]Department of Medical Research,China Medical University,Taichung,40402,Taiwan [4]Department of Mathematics and Statistics,Hazara University Mansehra,Mansehra,21300,Pakistan [5]Department of Mathematics,University of Malakand,Chakdara Dir(L),KPK,18000,Pakistan

出　　处：《Computer Modeling in Engineering & Sciences》2023年第7期901-919,共19页工程与科学中的计算机建模（英文）

摘　　要：In this paper,we establish the new forms of Riemann-type fractional integral and derivative operators.The novel fractional integral operator is proved to be bounded in Lebesgue space and some classical fractional integral and differential operators are obtained as special cases.The properties of new operators like semi-group,inverse and certain others are discussed and its weighted Laplace transform is evaluated.Fractional integro-differential freeelectron laser(FEL)and kinetic equations are established.The solutions to these new equations are obtained by using the modified weighted Laplace transform.The Cauchy problem and a growth model are designed as applications along with graphical representation.Finally,the conclusion section indicates future directions to the readers.

关 键 词：Weighted fractional operators weighted laplace transform integro-differential free-electron laser equation kinetic differ-integral equation 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]