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A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives

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Abstract.

This research article is analyzed for the comparative study of RL and RC electrical circuits by employing newly presented Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. The governing ordinary differential equations of RL and RC electrical circuits have been fractionalized in terms of fractional operators in the range of \(0 \leq \xi \leq 1\) and \(0 \leq \eta \leq 1\). The analytic solutions of fractional differential equations for RL and RC electrical circuits have been solved by using the Laplace transform with its inversions. General solutions have been investigated for periodic and exponential sources by implementing the Atangana-Baleanu and Caputo-Fabrizio fractional operators separately. The investigated solutions have been expressed in terms of simple elementary functions with convolution product. On the basis of newly fractional derivatives with and without singular kernel, the voltage and current have interesting behavior with several similarities and differences for the periodic and exponential sources.

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Authors and Affiliations

  1. Department of Basic Sciences and Related Studies, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Kashif Ali Abro

  2. Department of Electrical Engineering, Mehran University of Engineering and Technology, Jamshoro, Pakistan

    Anwar Ahmed Memon & Muhammad Aslam Uqaili

Authors
  1. Kashif Ali Abro
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  2. Anwar Ahmed Memon
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  3. Muhammad Aslam Uqaili
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Correspondence to Kashif Ali Abro.

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Abro, K.A., Memon, A.A. & Uqaili, M.A. A comparative mathematical analysis of RL and RC electrical circuits via Atangana-Baleanu and Caputo-Fabrizio fractional derivatives. Eur. Phys. J. Plus 133, 113 (2018). https://doi.org/10.1140/epjp/i2018-11953-8

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  • DOI: https://doi.org/10.1140/epjp/i2018-11953-8

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