TY - JOUR
T1 - Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense
AU - Coloma, Nicolás
AU - Di Teodoro, Antonio
AU - Ochoa-Tocachi, Diego
AU - Ponce, Francisco
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/9
Y1 - 2021/9
N2 - 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.
AB - 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.
KW - Bicomplex functions
KW - Bicomplex numbers
KW - Fractional Bicomplex functions
KW - Fractional Cauchy–Riemann operator
KW - Fractional analytic functions
UR - http://www.scopus.com/inward/record.url?scp=85112278392&partnerID=8YFLogxK
U2 - 10.1007/s00006-021-01165-0
DO - 10.1007/s00006-021-01165-0
M3 - Artículo
AN - SCOPUS:85112278392
SN - 0188-7009
VL - 31
JO - Advances in Applied Clifford Algebras
JF - Advances in Applied Clifford Algebras
IS - 4
M1 - 63
ER -