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Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense

Abstract:

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.