Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense

Nicolás Coloma; Antonio Di Teodoro; Diego Ochoa-Tocachi; Francisco Ponce

doi:10.1007/s00006-021-01165-0

Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense

Nicolás Coloma
, Antonio Di Teodoro^*
, Diego Ochoa-Tocachi
, Francisco Ponce

^*Corresponding author for this work

Matemáticas

Universidad San Francisco de Quito

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

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.

Original language	English
Article number	63
Journal	Advances in Applied Clifford Algebras
Volume	31
Issue number	4
DOIs	https://doi.org/10.1007/s00006-021-01165-0
State	Published - Sep 2021

Keywords

Bicomplex functions
Bicomplex numbers
Fractional Bicomplex functions
Fractional Cauchy–Riemann operator
Fractional analytic functions

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10.1007/s00006-021-01165-0

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title = "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.",

keywords = "Bicomplex functions, Bicomplex numbers, Fractional Bicomplex functions, Fractional Cauchy–Riemann operator, Fractional analytic functions",

author = "Nicol{\'a}s Coloma and \{Di Teodoro\}, Antonio and Diego Ochoa-Tocachi and Francisco Ponce",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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T1 - Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense

AU - Coloma, Nicolás

AU - Di Teodoro, Antonio

AU - Ochoa-Tocachi, Diego

AU - Ponce, Francisco

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 - https://www.scopus.com/pages/publications/85112278392

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 -

Fractional Elementary Bicomplex Functions in the Riemann–Liouville Sense

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Keywords

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