Analysis and Simulation of the RC Electrical Circuit Model Using Fractional Differential Equations (#1118)

Authors

Champi Apaza, Raul

Mollinedo Chura, Richar Marlon

Pumacallahui Salcedo, Eliseo

Ccama Alejo, Roger

Copari Romero, Fredy Gonzalo

Mamani Apaza, William Walker

Vilca Callata, Leonidas

Abstract

In this research work, the analytical solutions with Caputo and Caputo-Fabrizio derivative in the RC electric circuit model from integer order to fractional order were analyzed, with the objective of analyzing and simulating the RC electric circuit model by means of fractional order equations, so the RC electric circuit model was analyzed by different methods of solution of fractional order differential equations and the simulation of the RC electric circuit model was performed using Wolfram Mathematica 10.4 software. The methodology of this research is framed in the descriptive-deductive. For the modeling we used the physical laws and transition from the ordinary derivative operator to the fractional operator, then for the analytical solution we analyzed by means of the special Mittag-Leffler function, Laplace transform and the inverses of some functions. Finally, for the simulation of a constant source and periodic source of the RC electric circuit model of fractional order, the Wolfram Mathematica 10.4 software was used. The most relevant result is that an analogy was established between the ordinary differential equations and the fractional differential equations by means of Caputo and Caputo-Fabrizio fractional derivatives. This allowed to analyze the behavior of the RC electric circuit.