In this paper, we present the development of fractional bicomplex calculus in the Riemann–Liouville sense, based on the modification of the Cauchy–Riemann operator using the one-dimensional Riemann–Liouville derivative in each direction of the bicomplex basis. We introduce elementary functions such as analytic polynomials, exponential, trigonometric, and some properties of these functions. Furthermore, we present the fractional bicomplex Laplace operator connected with the fractional Cauchy–Riemann operator.

中文翻译：

---

Riemann-Liouville 意义上的分数基本双复形函数

在本文中，我们基于在双复基的每个方向上使用一维 Riemann-Liouville 导数对 Cauchy-Riemann 算子进行修改，介绍了 Riemann-Liouville 意义上的分数双复微积分的发展。我们介绍基本函数，例如解析多项式、指数、三角函数以及这些函数的一些性质。此外，我们提出了与分数 Cauchy-Riemann 算子相连的分数双复拉普拉斯算子。