NEW CONJECTURES FOR THE ENTIRE FUNCTIONS ASSOCIATED WITH FRACTIONAL CALCULUS

Xiao-Jun Yang
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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. China2Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia3Department of Mathematics, College of Science, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea

FRACTALS (fractals), 2024, vol. 32, issue 04, 1-7

Abstract: In this paper, we address the entire Fourier sine and cosine integrals related to the Mittag-Leffler function. We guess that the entire functions have the real zeros in the entire complex plane. They can be connected with the well-known conjectures in analytic number theory. They are considered as the special solutions for the time-fractional diffusion equation within the Caputo fractional derivative.

Keywords: Fourier Sine Integral; Fourier Cosine Integral; Time-Fractional Diffusion Equation; Mittag-Leffler Function; Analytic Number Theory; Caputo Fractional Derivative (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X23401291

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