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.

本文首次提出了Wiman类次三角函数、次双曲函数、预三角函数、准双曲函数、超三角函数和超双曲函数的许多重要公式。提出了与 Kohlrausch-Williams-Watts (KWW) 函数及其标度律 ODE 相关的亚正弦、亚余弦、亚双曲正弦和亚双曲余弦。获得与 Mittag-Leffler (ML) 函数相关的上正弦、上余弦、超双曲正弦和超双曲余弦函数及其分数 ODE。详细给出了包含ML函数的超余弦函数的猜想。