Fractional elementary bicomplex functions in the Riemann-Liouville sense (Q2049091)

The authors introduce a fractional bicomplex calculus in the Riemann-Liouville sense. This approach is based on a modification of the Cauchy-Riemann operator using the one-dimensional Riemann-Liouville derivative in each direction of the bicomplex basis. Elementary functions such as analytic polynomials, exponentials, trigonometric functions are defined and some of their properties are discussed. Furthermore, the fractional bicomplex Laplace operator connected with the fractional Cauchy-Riemann operator is presented.