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.

中文翻译：

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分数阶微积分全函数的新猜想

在本文中，我们讨论与 Mittag-Leffler 函数相关的整个傅里叶正弦和余弦积分。我们猜测整个函数在整个复平面上都有实零点。它们可以与解析数论中众所周知的猜想联系起来。它们被认为是 Caputo 分数阶导数内时间分数扩散方程的特殊解。