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A New Formulation And Analytical Applications Of Fractional Operators

Author

Listed:
  • 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)

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.

Suggested Citation

  • Ahsan Mehmood & Muhammad Samraiz & Zhi-Guo Liu & Dumitru Baleanu & Miguel Vivas-Cortez, 2025. "A New Formulation And Analytical Applications Of Fractional Operators," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(03), pages 1-13.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:03:n:s0218348x24501305
    DOI: 10.1142/S0218348X24501305
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