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Browsing by Author "Othmane, Iman ben"

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    Weighted Fractional Proportional Operators Regarding a Function and Their Hilfer Unification
    (World Scientific Publ Co Pte Ltd, 2025) Othmane, Iman ben; Abdeljawad, Thabet; Jarad, Fahd
    In this paper, some new forms of fractional operators are proposed. These new forms are developed by using the proportional and the weighted derivative of a function regarding a function, known as weighted fractional proportional operators regarding another function. Additionally, the partial derivative-Hilfer version of the weighted proportional fractional derivatives, which is a concept that unifies the Riemann-Liouville and Caputo weighted proportional fractional derivatives, is propounded. Moreover, a number of fundamental properties of these operators and related important results are investigated. The Laplace transforms of the newly defined operators are found. Finally, we solve a particular type of differential equations involving the introduced derivatives in favor of the weighted Laplace transform.