# Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Basic Definitions

## 3. Conformable Operator in the Caputo Sense

**Theorem**

**1.**

**Proof.**

## 4. Fractional Electrical Circuit and General Description of the Problem

_{αβ}have to be found based on measurements and fitting algorithms. Three series of measurements were taken and the average value of the results are presented in Table 1.

## 5. Conclusions

_{1}and C

_{2}, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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C_{1} (1 F) | C_{2} (0.33 F) | |||||
---|---|---|---|---|---|---|

Definition | α_{1} | β_{1} | C_{αβ}_{1} [F/s^{1−αβ}] | α_{1} | β_{1} | C_{αβ}_{2} [F/s^{1−αβ}] |

Classical case | 1.000 | 1.000 | 0.911 | 1.000 | 1.000 | 0.211 |

CFD | 1.000 | 0.761 | 0.424 | 1.000 | 0.761 | 0.091 |

Caputo | 0.857 | 1.000 | 0.431 | 0.857 | 1.000 | 0.062 |

CFD–Caputo | 0.914 | 0.884 | 0.412 | 0.914 | 0.884 | 0.071 |

Definition | C_{1} (1 F) | C_{2} (0.33 F) |
---|---|---|

χ^{2} | ||

Classical case | 47.2 | 46.5 |

CFD | 17.1 | 42.0 |

Caputo | 22.9 | 35.0 |

CFD–Caputo | 12.8 | 23.6 |

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**MDPI and ACS Style**

Piotrowska, E.; Sajewski, Ł.
Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense. *Symmetry* **2021**, *13*, 771.
https://doi.org/10.3390/sym13050771

**AMA Style**

Piotrowska E, Sajewski Ł.
Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense. *Symmetry*. 2021; 13(5):771.
https://doi.org/10.3390/sym13050771

**Chicago/Turabian Style**

Piotrowska, Ewa, and Łukasz Sajewski.
2021. "Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense" *Symmetry* 13, no. 5: 771.
https://doi.org/10.3390/sym13050771