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Weighted Fractional Proportional Operators Regarding A Function Andâ Their Hilfer Unification

Author

Listed:
  • IMAN BEN OTHMANE

    (Laboratory of Operators Theory and PDE)

  • THABET ABDELJAWAD

    (Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India3Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, Riyadh 11586, Saudi Arabia4Department of Medical Research, China Medical University, Taichung 40402, Taiwan5Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa6Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, South Korea)

  • FAHD JARAD

    (Department of Mathematics, Çankaya University, 06790 Ankara, Turkey8Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally 32093, Kuwait)

Abstract

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 ∂-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.

Suggested Citation

  • Iman Ben Othmane & Thabet Abdeljawad & Fahd Jarad, 2025. "Weighted Fractional Proportional Operators Regarding A Function Andâ Their Hilfer Unification," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-19.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:06:n:s0218348x25401152
    DOI: 10.1142/S0218348X25401152
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