The Q-Analogues Of Nonsingular Fractional Operators With Mittag-Leffler And Exponential Kernels

Sabri T.M. Thabet, Imed Kedim, Bahaaeldin Abdalla, Thabet Abdeljawad*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

This paper is devoted to introducing a new q-fractional calculus in the framework of Atangana-Baleanu (AB) and Caputo-Fabrizio (CF) operators. First, an appropriate q-Mittag-Leffler function is defined, and then q-analogues of fractional derivatives of Atangana-Baleanu-Riemann (ABR) and Atangana-Baleanu-Caputo (ABC) are derived. Next, the q-analogues of proper fractional integrals in the AB sense are proved. Several important properties of these definitions are investigated by using the q-Laplace transform. Additionally, a suitable q-exponential function is defined, and the q-analogues of CF fractional derivatives with their inverse operators are introduced. The higher-order extension of the q-analogues of AB and CF fractional operators is discussed. Finally, a demonstrative example is enhanced to check the effectiveness of q-ABC calculus. We believe that these outcomes will be the care of many researchers in the field of fractional calculus.

Original languageEnglish
Article number2440044
JournalFractals
Volume32
Issue number7-8
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • q-Atangana-Baleanu Fractional Operator
  • q-Caputo-Fabrizio Fractional Operator
  • q-Laplace Transformation
  • q-Mittag-Leffler Function

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