(1)Analysis of series RL and RC circuits with time-invariant source using truncated M, Atangana beta and conformable derivatives
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Sania Qureshia,∗, Mokhi Maan Changb, Asif Ali Shaikha
a Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology Jamshoro, 76062, Sindh, Pakistan
b Department of Electrical Engineering, Mehran University of Engineering and Technology Jamshoro, 76062, Sindh, Pakistan
Received 14 May 2020; received in revised form 23 November 2020; accepted 23 November 2020
Available online 24 November 2020
Abstract
Complex processes of the physical world require novel and sophisticated mathematical notions to get deep insights. In this research
analysis, two standard mathematical models for the series RL and RC circuits having time-invariant sources taken from the discipline
of electrical engineering have been investigated with the help of differential operators known with the name of truncated M- derivative,
Atangana beta-derivative, and the conformable derivative operators. The exact solutions for these two models have been found in terms of
the transcendental exponential function of time under the truncated M-derivative, Atangana beta-derivative, and the conformable derivative
operators. The numerical simulations carried out via MATLAB ”9.4.0.813654 (R2018a)” have been interpreted to explore new behavior for
solutions of the models not possible to obtain through standard classical calculus wherein one is restricted to have integer-order derivatives
unlike the differential operators used in the present research study. The models under consideration for the three differential operators have
been investigated with varying parameters’ values including the differential orders α and β whereupon the classical case is resumed for
α = β = 1 and τ = 0.
© 2020 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/)
Keywords: Mittag-Leffler function; M-integral; Constant voltage; Kirchoff’s laws; Numerical simulations.