THE Q-ANALOGUES OF NONSINGULAR FRACTIONAL OPERATORS WITH MITTAG-LEFFLER AND EXPONENTIAL KERNELS-Reference-Cited by-同舟云学术

THE Q-ANALOGUES OF NONSINGULAR FRACTIONAL OPERATORS WITH MITTAG-LEFFLER AND EXPONENTIAL KERNELS

Published:2024-07-03 Issue: Volume: Page:
ISSN:0218-348X
Container-title:Fractals
language:en
Short-container-title:Fractals

Author:

THABET SABRI T. M.¹²³^ORCID,KEDIM IMED⁴^ORCID,ABDALLA BAHAAELDIN⁵^ORCID,ABDELJAWAD THABET⁵⁶⁷⁸^ORCID

Affiliation:

1. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602 105, Tamil Nadu, India

2. Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen

3. Department of Mathematics, College of Science, Korea University, Seoul 02814, South Korea

4. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia

5. Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia

6. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

7. Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea

8. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa

Abstract

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

Funder

Prince Sattam bin Abdulaziz University

Publisher

World Scientific Pub Co Pte Ltd

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218348X24400449