Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel

By Abdon Atangana, J. J. Nieto. 2015

202 citations recorded by the source corpus.

The numerical approximation of the Caputo–Fabrizio fractional derivative with fractional order between 1 and 2 is proposed in this work. Using the transition from ordinary derivative to fractional derivative, we modified the RLC circuit model. The Crank–Nicolson numerical scheme was used to solve the modified model. We present the stability analysis of the numerical scheme for solving the modified equation and some numerical simulations for different values of the order of derivation.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/34587e5e5191da1c559a3ba8cc79d56c98cbfd38

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In Control and Systems Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Transient heat diffusion with a non-singular fading memory: From the Cattaneo constitutive equation with Jeffrey’s Kernel to the Caputo-Fabrizio time-fractional derivative (2016, background): “The Caputo-Fabrizio time-fractional derivative immediately attracted the interest of the researchers and for about a year after the seminal publication [1] numerous applications have been reported, among them: elasticity [4], resistance and numerical modelling of fractional electric circuit [5, 6], ”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “Recently, Caputo and Fabrizio [12] and Atangana and Baleanu [7] proposed some interesting fractional-order derivatives based upon the exponential decay law which is a generalized power-law function (see [1, 3, 4, 5, 6, 8]).”
New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model (2016, background): “Introduction A new derivative was recently launched by Caputo and Fabrizio [1] and it was followed by some related theoretical and applied results (for example [2-4] and the references therein).”
Application of the Caputo-Fabrizio Fractional Derivative without Singular Kernel to Korteweg-de Vries-Burgers Equation∗ (2016, methodology): “the authors in [3] were able to prove the following theorem: Theorem 1.”
Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative (2019, background): “Losada, J.; Nieto, J.J. Properties of a new fractional derivative without singular kernel.”