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Calculus Operators And Special Functions Associated With Kohlrausch–Williams–Watts And Mittag-Leffler Functions

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  • XIAO-JUN YANG

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China†Department of Mathematics, Faculty of Science, King Abdulaziz University P. O. Box 80257, Jeddah 21589, Saudi Arabia‡Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea)

  • LU-LU GENG

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

  • YU-MEI PAN

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

  • XIAO-JIN YU

    (State Key Laboratory of Intelligent Construction and Healthy Operation and Maintenance of Deep Underground Engineering and School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China)

Abstract

In this paper, many important formulas of the subtrigonometric, subhyperbolic, pretrigonometric, prehyperbolic, supertrigonometric, and superhyperbolic functions sin Wiman class are developed for the first time. The subsine, subcosine, subhyperbolic sine, and subhyperbolic cosine associated with Kohlrausch–Williams–Watts (KWW) function and their scaling-law ODEs are proposed. The supersine, supercosine, superhyperbolic sine, and superhyperbolic cosine functions associated with Mittag-Leffler (ML) function and their fractional ODEs are obtained. The conjectures for the supercosine functions containing ML function are presented in detail.

Suggested Citation

  • Xiao-Jun Yang & Lu-Lu Geng & Yu-Mei Pan & Xiao-Jin Yu, 2024. "Calculus Operators And Special Functions Associated With Kohlrausch–Williams–Watts And Mittag-Leffler Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(04), pages 1-30.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:04:n:s0218348x23401321
    DOI: 10.1142/S0218348X23401321
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