Abstract
In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each other and with the usual solutions. Finally, they are compared with practical and laboratory results.
Highlights
The idea of fractional calculus coincides with that of classical calculus
5 Conclusion In order to find the transient response of the parallel RCL Circuit with Caputo–Fabrizio derivative and use of the inverse Laplace transformations when only the inductor has primary energy, it gives an obvious response, but it is used to find s1 and s2 in the equation V (t) = A1es1t + A2es2t
When the capacitor has primary energy, the transient response is obtained with the Laplace transforms and the inverse Laplace transformations
Summary
The idea of fractional calculus coincides with that of classical calculus. Leibniz and l’Hopital first raised this issue in 1695 and in 1730 Euler’s attention was drawn to it, followed by Lagrange in 1772 and Laplace in 1812. In 2015 Caputo and Fabrizio introduced a new fractional derivative using the exponential function. This derivative has no singularity [20] and [36]. In [5] the advantages of the new differential operators are explained Following this same process, Atangana and Baleanu introduced another derivative of Caputo–Fabrizio by introducing the Mittag-Leffler function into the fractional derivative, which many researchers have used in their papers. New extensions and generalizations of the Caputo–Fabrizio derivative and other fractional derivatives can be found in articles [10, 11, 14,15,16].
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