Skip to main content
SpringerLink
Log in

Analytical solutions of electrical circuits considering certain generalized fractional derivatives

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. Sun, Y. Zhang, D. Baleanu, W. Chen, Y. Chen, Commun. Nonlinear Sci. Numer. Simul. 64, 213 (2018)

    Article  ADS  Google Scholar 

  2. R.L. Bagley, P.J. Torvik, J. Rheol. 27, 201 (1983)

    Article  ADS  Google Scholar 

  3. N. Sene, Chaos, Solitons Fractals 117, 68 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  4. F. Shen, W. Tan, Y. Zhao, T. Masuoka, Nonlinear Anal.: Real World Appl. 7, 1072 (2006)

    Article  MathSciNet  Google Scholar 

  5. V.F. Morales-Delgado, J.F. Gómez-Aguilar, K.M. Saad, M.A. Khan, P. Agarwal, Physica A 523, 48 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  6. M.A. Khan, Chaos 29, 013144 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  7. M.M. El-Dessoky, M.A. Khan, Chaos 29, 013107 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  8. M.A. Khan, M. Farhan, S. Islam, E. Bonyah, Discr. Contin. Dyn. Syst. S 12, 455 (2019)

    Google Scholar 

  9. T. Gul, M.A. Khan, A. Khan, M. Shuaib, Eur. Phys. J. Plus 133, 500 (2018)

    Article  Google Scholar 

  10. S. Ullah, M.A. Khan, M. Farooq, Eur. Phys. J. Plus 133, 237 (2018)

    Article  Google Scholar 

  11. A. Atangana, D. Baleanu, Therm. Sci. 20, 763 (2016)

    Article  Google Scholar 

  12. U.N. Katugampola, Appl. Math. Comput. 218, 860 (2011)

    MathSciNet  Google Scholar 

  13. M. Caputo, M. Fabrizio, Progr. Fract. Differ. Appl. 1, 73 (2015)

    Google Scholar 

  14. A. Atangana, B.S.T. Alkahtani, Adv. Mech. Eng. (2015) https://doi.org/10.1177/1687814015591937

  15. H. Ertik, A.E. Calik, H. Sirin, M. Sen, B. Öder, Rev. Mex. Fis. 61, 58 (2015)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  18. P.V. Shah, A.D. Patel, I.A. Salehbhai, A.K. Shukla, Abstr. Appl. Anal. 2014, 343814 (2014)

    Article  Google Scholar 

  19. V.F. Morales-Delgado, J.F. Gómez-Aguilar, M.A. Taneco-Hernández, AEU Int. J. Electron. Commun. 85, 108 (2018)

    Article  Google Scholar 

  20. A. Alsaedi, J.J. Nieto, V. Venktesh, Adv. Mech. Eng. (2015) https://doi.org/10.1177/1687814015618127

  21. J.P. Chauhan, P.V. Shah, R.K. Jana, A.K. Shukla, Ital. J. Pure Appl. Math. 36, 819 (2016)

    Google Scholar 

  22. F. Jarad, T. Abdeljawad, Results Nonlinear Anal. 1, 88 (2018)

    Google Scholar 

  23. A.A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier Science, 2006)

  24. N. Sene, Fractal Fract. 2, 17 (2018)

    Article  Google Scholar 

  25. Y. Adjabi, F. Jarad, T. Abdeljawad, Filomat 31, 5457 (2017)

    Article  MathSciNet  Google Scholar 

  26. Y.Y. Gambo, R. Ameen, F. Jarad, T. Abdeljawad, Adv. Differ. Equ. 2018, 134 (2018)

    Article  Google Scholar 

  27. F. Jarad, E. Ugurlu, T. Abdeljawad, D. Baleanu, Adv. Differ. Equ. 2017, 247 (2017)

    Article  Google Scholar 

  28. N. Sene, Prog. Fract. Differ. Appl. 4, 493 (2018)

    Google Scholar 

  29. S. Priyadharsini, J. Fract. Calculus Appl. 7, 87 (2016)

    MathSciNet  Google Scholar 

  30. E.F. Doungmo Goufo, Chaos 26, 084305 (2016)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire Lmdan, Département de Mathématiques de la Décision, Université Cheikh Anta Diop de Dakar, Faculté des Sciences Economiques et Gestion, BP 5683, Dakar Fann, Senegal

    Ndolane Sene

  2. CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico

    J. F. Gómez-Aguilar

Authors
  1. Ndolane Sene
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. F. Gómez-Aguilar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. F. Gómez-Aguilar.

Additional information

Publisher's Note

The EPJ Publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sene, N., Gómez-Aguilar, J.F. Analytical solutions of electrical circuits considering certain generalized fractional derivatives. Eur. Phys. J. Plus 134, 260 (2019). https://doi.org/10.1140/epjp/i2019-12618-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2019-12618-x

Search

Navigation