A NEW FORMULATION AND ANALYTICAL APPLICATIONS OF FRACTIONAL OPERATORS

Ahsan Mehmood (), Muhammad Samraiz (), Zhi-Guo Liu (), Dumitru Baleanu and Miguel Vivas-Cortez
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Ahsan Mehmood: School of Mathematical Sciences and Shanghai Key Labortary PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, P. R. China
Muhammad Samraiz: ��Department of Mathematics, University of Sargodha, P. O. Box 40100, Sargodha, Pakistan
Zhi-Guo Liu: School of Mathematical Sciences and Shanghai Key Labortary PMMP, East China Normal University, 500 Dongchuan Road, Shanghai 200241, P. R. China
Dumitru Baleanu: ��Department of Computer Science and Mathematics, Lebanese American University, Beirut§Lebanon Institute of Space Sciences, Magurele-Bucharest 077125, Romania
Miguel Vivas-Cortez: �Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Ecuador

FRACTALS (fractals), 2025, vol. 33, issue 03, 1-13

Abstract: This research paper introduces a novel formulation of the modified Atangana–Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.

Keywords: Fractional Calculus Operators; Differential Equation; Laplace Transform; Mittag-Leffler (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X24501305

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