Muhammad Samraiz1, Muhammad Umer1, Thabet Abdeljawad2,3,*, Saima Naheed1, Gauhar Rahman4, Kamal Shah2,5
CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 901-919, 2023, DOI:10.32604/cmes.2023.024029
Abstract 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 free-electron 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… More >
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