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Search Results (3)

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Keywords = fractional-order electrical RLC-circuit equations

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22 pages, 677 KiB  
Article
The LDG Finite-Element Method for Multi-Order FDEs: Applications to Circuit Equations
by Mohammad Izadi, Hari Mohan Srivastava and Mahdi Kamandar
Fractal Fract. 2025, 9(4), 230; https://doi.org/10.3390/fractalfract9040230 - 5 Apr 2025
Viewed by 433
Abstract
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the [...] Read more.
The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article
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16 pages, 781 KiB  
Article
Numerical Solutions of Fractional-Order Electrical RLC Circuit Equations via Three Numerical Techniques
by Uroosa Arshad, Mariam Sultana, Ali Hasan Ali, Omar Bazighifan, Areej A. Al-moneef and Kamsing Nonlaopon
Mathematics 2022, 10(17), 3071; https://doi.org/10.3390/math10173071 - 25 Aug 2022
Cited by 24 | Viewed by 3567
Abstract
In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional [...] Read more.
In this article, three different techniques, the Fractional Perturbation Iteration Method (FPIA), Fractional Successive Differentiation Method (FSDM), and Fractional Novel Analytical Method (FNAM), have been introduced. These three iterative methods are applied on different types of Electrical RLC-Circuit Equations of fractional-order. The fractional series approximation of the derived solutions can be established by using the obtained coefficients. These three algorithms handle the problems in a direct manner without any need for restrictive assumptions. The comparison displays an agreement between the obtained results. The beauty of this paper lies in the error analysis between the exact solution and approximate solutions obtained by these three methods which prove that the Approximate Solution obtained by FNAM converge very rapidly to the exact solution. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)
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12 pages, 572 KiB  
Article
Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels
by José Francisco Gómez-Aguilar, Victor Fabian Morales-Delgado, Marco Antonio Taneco-Hernández, Dumitru Baleanu, Ricardo Fabricio Escobar-Jiménez and Maysaa Mohamed Al Qurashi
Entropy 2016, 18(8), 402; https://doi.org/10.3390/e18080402 - 20 Aug 2016
Cited by 111 | Viewed by 11332
Abstract
In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville–Caputo, Caputo–Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source [...] Read more.
In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville–Caputo, Caputo–Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order α is equal to 1. Full article
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory II)
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