Generalized Fractional Cauchy–Riemann Operator Associated with the Fractional Cauchy–Riemann Operator

We present the development of fractional generalized complex calculus in the Riemann-Liouville sense, modifying the Cauchy-Riemann operator using the one-dimensional Riemann-Liouville derivative. We analyze the properties of the correspondent fractional analytic functions and introduce a family of analytic polynomials which are necessary to construct series expansions. We provide examples and visuals of these polynomials and use them to solve fractional differential equations and verify fractional Leibniz rule numerically.

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“…In this section, we define generalized complex polynomials based on well known results of the complex case studied in [4].…”

Section: Fractional Polynomialsmentioning

confidence: 99%

A family of fractional analytic polynomials in generalized complex numbers and applications

Teodoro

Morillo

Ochoa-Tocachi

et al. 2023

Preprint

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“…From an operator's point of view (see [44], [46], [51]), the real differential property lim α→1 − RL D α…”

Section: B Behavior Of the Fractional Parameter αmentioning

confidence: 99%

A New Fractional Reduced-Order Model-Inspired System Identification Method for Dynamical Systems

Gude,

Di Teodoro,

Camacho

et al. 2023

IEEE Access

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This paper presents a new method for identifying dynamical systems to get fractionalreduced-order models based on the process reaction curve. This proposal uses information collected from the process. It can be applied to processes with an S-shaped step response that can be considered with fractional behavior and a fractional order range of α ∈ [0.5, 1.0]. The proposed approach combines obtaining model fractional order using asymptotic properties of the Mittag-Leffler function with time-based parameter estimation by considering two arbitrary points on the process reaction curve. The improvement in terms of accuracy of the identified FFOPDT model is obtained due to a more accurate estimation of α parameter. This method is characterized by its effectiveness and simplicity of implementation, which are key aspects when applying at an industrial level. Several examples are used to illustrate the effectiveness and simplicity of the proposed method compared to other well-established methods and other approaches based on the process reaction curve. Finally, it is also implemented on microprocessor-based hardware to demonstrate the applicability of the proposed method to identify the fractional model of a thermal process.INDEX TERMS fractional-order systems, process identification, fractional first-order plus dead-time model.

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“…[3][4][5][6][7][8] For a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering, we refer the reader to de Oliveira and Tenreiro Machado. 9 A framework for a fractional Euclidian Clifford analysis represents a very recent topic of research; see other works [10][11][12][13][14] and the references given there. In particular, the interest for considering fractional Dirac Operator is devoted in other studies.…”

Section: Introductionmentioning

confidence: 99%

“…A framework for a fractional Euclidian Clifford analysis represents a very recent topic of research; see other works 10–14 and the references given there. In particular, the interest for considering fractional Dirac Operator is devoted in other studies 15–18 …”

Section: Introductionmentioning

confidence: 99%

A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function

González-Cervantes

Reyes

2022

Math Methods in App Sciences

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Generalized Fractional Cauchy–Riemann Operator Associated with the Fractional Cauchy–Riemann Operator

Cited by 9 publications

References 37 publications

A family of fractional analytic polynomials in generalized complex numbers and applications

A family of fractional analytic polynomials in generalized complex numbers and applications

A New Fractional Reduced-Order Model-Inspired System Identification Method for Dynamical Systems

A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function

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