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Analytical solutions of electrical circuits considering certain generalized fractional derivatives

  • Ndolane Sene
  • J. F. Gómez-AguilarEmail author
Regular Article
  • 18 Downloads

Abstract.

The paper addresses the analytical solutions for the RL, LC, RC and RLC electrical circuits described by the left generalized fractional derivative operator and the Caputo left generalized fractional derivative. The \( \rho\)-Laplace transform introduced by Fahd and Thabet was used to obtain the analytical solutions of the electrical circuit equations described by certain generalized fractional derivative operators. Finally, we present some numerical simulations of the analytical solutions of the RL, LC, RC and RLC electrical circuit equations described by certain generalized fractional derivatives.

References

  1. 1.
    H. Sun, Y. Zhang, D. Baleanu, W. Chen, Y. Chen, Commun. Nonlinear Sci. Numer. Simul. 64, 213 (2018)CrossRefGoogle Scholar
  2. 2.
    R.L. Bagley, P.J. Torvik, J. Rheol. 27, 201 (1983)CrossRefGoogle Scholar
  3. 3.
    N. Sene, Chaos, Solitons Fractals 117, 68 (2018)MathSciNetCrossRefGoogle Scholar
  4. 4.
    F. Shen, W. Tan, Y. Zhao, T. Masuoka, Nonlinear Anal.: Real World Appl. 7, 1072 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    V.F. Morales-Delgado, J.F. Gómez-Aguilar, K.M. Saad, M.A. Khan, P. Agarwal, Physica A 523, 48 (2019)MathSciNetCrossRefGoogle Scholar
  6. 6.
    M.A. Khan, Chaos 29, 013144 (2019)MathSciNetCrossRefGoogle Scholar
  7. 7.
    M.M. El-Dessoky, M.A. Khan, Chaos 29, 013107 (2019)MathSciNetCrossRefGoogle Scholar
  8. 8.
    M.A. Khan, M. Farhan, S. Islam, E. Bonyah, Discr. Contin. Dyn. Syst. S 12, 455 (2019)Google Scholar
  9. 9.
    T. Gul, M.A. Khan, A. Khan, M. Shuaib, Eur. Phys. J. Plus 133, 500 (2018)CrossRefGoogle Scholar
  10. 10.
    S. Ullah, M.A. Khan, M. Farooq, Eur. Phys. J. Plus 133, 237 (2018)CrossRefGoogle Scholar
  11. 11.
    A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)CrossRefGoogle Scholar
  12. 12.
    U.N. Katugampola, Appl. Math. Comput. 218, 860 (2011)MathSciNetGoogle Scholar
  13. 13.
    M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 1, 73 (2015)Google Scholar
  14. 14.
    A. Atangana, B.S.T. Alkahtani, Adv. Mech. Eng. (2015)  https://doi.org/10.1177/1687814015591937
  15. 15.
    H. Ertik, A.E. Calik, H. Sirin, M. Sen, B. Öder, Rev. Mex. Fis. 61, 58 (2015)Google Scholar
  16. 16.
    J.F. Gómez-Aguilar, V.F. Morales-Delgado, M.A. Taneco-Hernández, D. Baleanu, R.F. Escobar-Jiménez, M.M. Al Qurashi, Entropy 18, 402 (2016)CrossRefGoogle Scholar
  17. 17.
    J.F. Gómez-Aguilar, H. Yépez-Martínez, R.F. Escobar-Jiménez, C.M. Astorga-Zaragoza, J. Reyes-Reyes, Appl. Math. Model. 40, 9079 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    P.V. Shah, A.D. Patel, I.A. Salehbhai, A.K. Shukla, Abstr. Appl. Anal. 2014, 343814 (2014)CrossRefGoogle Scholar
  19. 19.
    V.F. Morales-Delgado, J.F. Gómez-Aguilar, M.A. Taneco-Hernández, AEU Int. J. Electron. Commun. 85, 108 (2018)CrossRefGoogle Scholar
  20. 20.
    A. Alsaedi, J.J. Nieto, V. Venktesh, Adv. Mech. Eng. (2015)  https://doi.org/10.1177/1687814015618127
  21. 21.
    J.P. Chauhan, P.V. Shah, R.K. Jana, A.K. Shukla, Ital. J. Pure Appl. Math. 36, 819 (2016)Google Scholar
  22. 22.
    F. Jarad, T. Abdeljawad, Results Nonlinear Anal. 1, 88 (2018)Google Scholar
  23. 23.
    A.A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science, 2006)Google Scholar
  24. 24.
    N. Sene, Fractal Fract. 2, 17 (2018)CrossRefGoogle Scholar
  25. 25.
    Y. Adjabi, F. Jarad, T. Abdeljawad, Filomat 31, 5457 (2017)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Y.Y. Gambo, R. Ameen, F. Jarad, T. Abdeljawad, Adv. Differ. Equ. 2018, 134 (2018)CrossRefGoogle Scholar
  27. 27.
    F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, Adv. Differ. Equ. 2017, 247 (2017)CrossRefGoogle Scholar
  28. 28.
    N. Sene, Prog. Fract. Differ. Appl. 4, 493 (2018)Google Scholar
  29. 29.
    S. Priyadharsini, J. Fract. Calculus Appl. 7, 87 (2016)MathSciNetGoogle Scholar
  30. 30.
    E.F. Doungmo Goufo, Chaos 26, 084305 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et GestionDakar FannSenegal
  2. 2.CONACyT-Tecnológico Nacional de México/CENIDETCuernavacaMexico

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