Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method

Abstract

In the presented work, we present an accurate procedure, which is the spectral method, to find a solution to a certain class of the very important fractional (described by the Liouville-Caputo sense) models of the electrical RL, RC, and RLC circuits. This method is collocated using some important advantages of the generalized Legendre polynomials to obtain the numerical solution for these models. Besides, we compare the approximate solutions that are obtained using the presented technique for the proposed models with their exact solution in the given numerical examples.

Analysis of time‐domain response of series‐parallel fractional‐order RCα and RLβ circuits based on Cole distribution function

“…In sum, practical applications of the SPFOC discretization procedure includes the following four steps: First, the parameter λ and ω max should be defined in advance according to practical application situations; second, K is calculated by (18) based on the pre-defined discretization parameters (λ and ω max ) and the time constant of SPFOC (τ 0 ); third, the time constant τ k for the kth first-order circuit is calculated by (17); finally, the transfer function of SPFOC can be discretized in (16) as the sum of the first-order expressions.…”

“…Recently, Gómez‐Aguilar et al propose an analytical TDR solution for the series fractional‐order , and circuits described by Atangana–Baleanu fractional derivatives 17 . Later, the same group 18 proposes a Legendre pseudo‐spectral method to present a numerical TDR solution for serial fractional‐order circuits.…”

Implementation of an accurate method for the analysis and simulation of electrical R‐L circuits

“…There have been many studies that have used estimation-oriented and computational methods to simulate and analyze fractional differential equations (FDEs). [1][2][3][4] Mathematicians and others interested in applied science are paying close attention to this area of research. [5][6][7][8][9][10] It is due to the importance of this type of equations in many applications.…”

Modeling and Numerical Simulation for Covering the Fractional COVID-19 Model Using Spectral Collocation-Optimization Algorithm

“…Finding a novel fractional derivative with non-singular kernels is critical, according to some writers, to address the demand for mathematical modeling of numerous real-world situations in various sectors of daily life [19,20]. Also, the role of these new operators are appearing in many applications like engineering, chemistry, electricity, and many other applications [21,22]. Because fractional differential equations (FDEs) rarely have a precise solution, they are frequently studied using approximate techniques [23][24][25].…”

“…For more properties, and theoretical results [19,20]. Many researchers have presented a variety of numerical techniques to study and simulate the behavior of solutions for differential equations, including the finite difference method [25], the finite volume method [28], spectral methods [29], and many others [22,30]. One of the most effective techniques for simulating FDEs is the spectral approaches.…”