Analysis of series RL and RC circuits with time-invariant source using truncated M, Atangana beta and conformable derivatives

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.

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