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A numerical study of anomalous electro-diffusion cells in cable sense with a non-singular kernel

100%

Iqbal A. , Akram T.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

574--586

The time-fractional cable model is solved using an extended cubic B-spline (ECBS) collocation strategy. The B-spline function was used for space partitioning, while the Caputo-Fabrizio (CF) was used for temporal discretization. The finite difference technique was used to discretize the CF operator. For the first time in cable modeling, the CF operator has been used. In terms of time, the convergence of order τ . An ECBS collocation approach is investigated by numerical example at different values, and comparisons with published work are made. The numerical results show that the scheme performed well, and the graphical representations show that the results are very close to exact values. The Von Neumann technique is applied to investigate the stability of the proposed scheme.

Fractional-order model of a non-linear inductor

100%

Lopes A. M. , Tenreiro-Machado J. A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2019

tom Vol. 67, nr 1

61--67

This paper adopts a fractional calculus perspective to describe a non-linear electrical inductor. First, the electrical impedance spectroscopy technique is used for measuring the impedance of the device. Second, the experimental data is approximated by means of fractional-order models. The results demonstrate that the proposed approach represents the inductor using a limited number of parameters, while highlighting its most relevant characteristics.

Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

67%

Maitama S. , Zhao W.

Journal of Applied Mathematics and Computational Mechanics

2021

tom Vol. 20, nr 1

71--82

Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He’s polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.