Results 191 to 200 of about 3,215 (223)

Misconceptions in using Riemann-Liouville’s and Caputo’s definitions for the description and initialization of fractional partial differential equations

IFAC-PapersOnLine, 2017
Abstract In this paper, it is shown that neither Riemann-Liouville’s nor Caputo’s definitions can be used to properly take into account initial conditions in the description of a fractional partial differential equation. This demonstration is done on a counterexample. Some suggestions are made to address this problem.
Christophe Farges, Jocelyn Sabatier
exaly   +2 more sources

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CHARACTERISTIC ANALYSIS OF FRACTIONAL-ORDER RLC CIRCUIT BASED ON THE CAPUTO–FABRIZIO DEFINITION

Fractals, 2022
The Caputo–Fabrizio (C–F) definition, which solves the singularity problem in the Caputo definition, has been preliminarily applied in the field of circuit system modeling. However, the complex characteristics of the C–F definition-based circuit systems are still understudied.
XIAOZHONG LIAO, DONGHUI YU, DA LIN, MANJIE RAN, JINHUI XIA   +4 more
openaire   +1 more source

ANALOG IMPLEMENTATION OF FRACTIONAL-ORDER ELECTRIC ELEMENTS USING CAPUTO–FABRIZIO AND ATANGANA–BALEANU DEFINITIONS

Fractals, 2021
This study employs the Caputo–Fabrizio and Atangana–Baleanu fractional derivatives to determine the impedance and admittance model of fractional capacitor and inductor. The analog implementation circuits are proposed aiming at fractional-order electric elements based on these two derivatives, which can be widely used in a variety of electrical systems ...
XIAOZHONG LIAO, DA LIN, LEI DONG, MANJIE RAN, DONGHUI YU   +4 more
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A new modified definition of Caputo–Fabrizio fractional-order derivative and their applications to the Multi Step Homotopy Analysis Method (MHAM)

Journal of Computational and Applied Mathematics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huitzilin Yépez-Martínez, J F Gómez-Aguilar   +1 more
exaly   +2 more sources

A novel definition of the caputo fractional finite difference approach for Maxwell fluid

Computational and Applied Mathematics
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Muhammad Imran Asjad, Tamour Zubair, Syeda Alishwa Zanib   +2 more
exaly   +4 more sources

Numerical Approximation of Caputo Definition and Simulation of Fractional PID Controller

2020
Caputo definition of Fractional Diffintegration is numerically approximated for the real-time implementation in the digital/Computer/Embedded system. Fractional numerical methods and properties are discussed in this paper and the new method of software implementation is suggested for the fractional Proportional Integral-Derivative (PID) Controller ...
Sachin Gade, Mahesh Kumbhar, Sanjay Pardeshi   +2 more
openaire   +1 more source

Analysis of fractional capacitor and coil by the use of the Conformable Fractional Derivative and Caputo definitions

2018 International Interdisciplinary PhD Workshop (IIPhDW), 2018
This paper deals with the analysis of the electrical circuit with the fractional capacitor as well as the coils described by the fractional order state space equations in the transient state. There are two types of definitions of fractional derivative used in the fractional state space equations which are general solutions.
Ewa Piotrowska
exaly   +2 more sources

Caputo definition for finding fractional moments of power law distribution functions

2022
In this paper, we propose a modern technique to derive fractional moment by using Caputo definition of fractional derivative.  Such technique represents a modification of fractional moments on a certain type of function which is known by the power law distribution functions.
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Analysis of Fractional Electrical Circuit Using Caputo and Conformable Derivative Definitions

2018
The paper presents an analysis of the fractional electrical circuit in the transient state described by the fractional-order state-space equations. General solutions to the fractional state-space equations containing two types of definitions of fractional derivative: Caputo fractional order derivative and the Conformable Fractional Derivative (CFD ...
Ewa Piotrowska, Krzysztof Rogowski
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FoGDbED: Fractional-order Gaussian derivatives-based edge-relevant structure detection using Caputo-Fabrizio definition

Digital Signal Processing, 2020
Abstract Edge-relevant structure features (ERSFs), e.g., object edges, boundaries and contours, junctions, etc. play an important role in low and middle level image processing tasks, such as image segmentation, as well as in higher-level computer vision tasks, such as scene analysis and content understanding.
Guoyong Zhang, Jinping Liu 0003, Jie Wang 0150, Zhaohui Tang 0004, Yongfang Xie, Junbin He, Tianyu Ma, Jean Paul Niyoyita   +7 more
openaire   +2 more sources