2023
DOI: 10.32604/cmes.2023.024029
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On Riemann-Type Weighted Fractional Operators and Solutions to Cauchy Problems

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 freeelectron laser (FEL) and kinetic equations are established… Show more

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Cited by 5 publications
(4 citation statements)
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“…Also, the operators with fractional order have a greater degree of freedom and therefore are increasingly used to describe various real world problems. Some important work recently published using fractional order derivatives include [27][28][29][30].…”
Section: Related Workmentioning
confidence: 99%
“…Also, the operators with fractional order have a greater degree of freedom and therefore are increasingly used to describe various real world problems. Some important work recently published using fractional order derivatives include [27][28][29][30].…”
Section: Related Workmentioning
confidence: 99%
“…It is a relatively new field of study that has gained significant attention from researchers because of its wide-ranging applications in different sectors of science and engineering [ [1] , [2] , [3] , [4] , [5] ]. This has resulted in the development of new mathematical tools and techniques that have been used to solve complex problems in physics, engineering, finance, and other fields [ [6] , [7] , [8] , [9] , [10] ]. Studying fractional calculus has yielded the maturation of numerous numerical strategies for solving fractional models, including Riemann, Caputo, and Grunwald-Letnikov's approaches [ [11] , [12] , [13] ].…”
Section: Introductionmentioning
confidence: 99%
“…In recent years, the area related to fractional differential and integral equations has received much attention from numerous mathematicians and specialists [1]. The derivatives of fractional order represent physical models of multiple phenomena in many fields, including engineering [2,3], mathematical physics [4], fractional calculus [5] and bio-engineering [6]. The idea of convexity has been modernized, extended and expanded in several ways [7,8].…”
Section: Introductionmentioning
confidence: 99%