TY  - EJOU
AU  - Samraiz, Muhammad 
AU  - Umer, Muhammad 
AU  - Abdeljawad, Thabet 
AU  - Naheed, Saima 
AU  - Rahman, Gauhar 
AU  - Shah, Kamal 

TI  - On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2023
VL  - 136
IS  - 1
SN  - 1526-1506

AB  - 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 representation. Finally, the conclusion section indicates future directions to the readers.
KW  - Weighted fractional operators; weighted laplace transform; integro-differential free-electron laser equation; kinetic differ-integral equation

DO  - 10.32604/cmes.2023.024029