Analysis and Simulation of RC Electric Circuit Model by Fractional Differential Equations

Champi Apaza R.; Marlon Mollinedo Chura R.; Pumacallahui Salcedo E.; Ccama Alejo R.; Gonzalo Copari Romero F.; Walker Mamani Apaza W.; Vilca Callata L. · Proceedings of the LACCEI international Multi-conference for Engineering, Education and Technology (2025) · DOI: 10.18687/laccei2025.1.1.1118

Resumen

In this research work, the analytical solutions with Caputo and Caputo-Fabrizio derivative were analyzed in the RC electric circuit model from integer order to fractional order, 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, the physical laws and the transition from the ordinary derivative operator to the fractional operator were used, then for the analytical solution it was 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.

Instituciones: Universidad Nacional del Altiplano; Universidad Nacional Intercultural de Quillabamba