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

Muhammad Samraiz1, Muhammad Umer1, Thabet Abdeljawad2,3,*, Saima Naheed1, Gauhar Rahman4, Kamal Shah2,5

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

* Corresponding Author: Thabet Abdeljawad. Email: email

(This article belongs to the Special Issue: Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)

Computer Modeling in Engineering & Sciences 2023, 136(1), 901-919. https://doi.org/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 representation. Finally, the conclusion section indicates future directions to the readers.

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APA Style
Samraiz, M., Umer, M., Abdeljawad, T., Naheed, S., Rahman, G. et al. (2023). On riemann-type weighted fractional operators and solutions to cauchy problems. Computer Modeling in Engineering & Sciences, 136(1), 901-919. https://doi.org/10.32604/cmes.2023.024029
Vancouver Style
Samraiz M, Umer M, Abdeljawad T, Naheed S, Rahman G, Shah K. On riemann-type weighted fractional operators and solutions to cauchy problems. Comput Model Eng Sci. 2023;136(1):901-919 https://doi.org/10.32604/cmes.2023.024029
IEEE Style
M. Samraiz, M. Umer, T. Abdeljawad, S. Naheed, G. Rahman, and K. Shah "On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems," Comput. Model. Eng. Sci., vol. 136, no. 1, pp. 901-919. 2023. https://doi.org/10.32604/cmes.2023.024029



cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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