TY - UNPB
T1 - A quaternionic proportional fractional Fueter-type operator calculus
AU - González-Cervantes, J. Oscar
AU - Bory Reyes, Juan
PY - 2023/6/14
Y1 - 2023/6/14
N2 - The main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional fractional integral and derivative with respect to a real-valued function via the Riemann-Liouville fractional derivative. As a main result, we prove a quaternionic proportional fractional Borel-Pompeiu formula based on a quaternionic proportional fractional Stokes formula. This tool in hand allows us to present a Cauchy integral type formula for the introduced quaternionic proportional fractional Fueter-type operator with respect to a real-valued function.
AB - The main goal of this paper is to construct a proportional analogues of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional fractional integral and derivative with respect to a real-valued function via the Riemann-Liouville fractional derivative. As a main result, we prove a quaternionic proportional fractional Borel-Pompeiu formula based on a quaternionic proportional fractional Stokes formula. This tool in hand allows us to present a Cauchy integral type formula for the introduced quaternionic proportional fractional Fueter-type operator with respect to a real-valued function.
KW - Quaternionic analysis, Fractional Fueter operator, Proportional fractional integrals and derivatives
M3 - Documento de trabajo
T3 - ArXiv
SP - 1
EP - 20
BT - A quaternionic proportional fractional Fueter-type operator calculus
ER -