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Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives

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

Special Issues: New trends of numerical and analytical methods with application to real world models for instance RLC with new nonlocal operators

The fractional input stability of the electrical circuit equations described by the fractional derivative operators has been investigated. The Riemann-Liouville and the Caputo fractional derivative operators have been used. The analytical solutions of the electrical circuit equations have been developed. The Laplace transforms of the Riemann-Liouville, and the Caputo fractional derivative operators have been used. The graphical representations of the analytical solutions of the electrical circuit equations have been presented. The converging-input converging-state property of the electrical RL, RC and LC circuit equations described by the Caputo fractional derivative, and the global asymptotic stability property of the unforced electrical circuit equations have been illustrated.
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Keywords fractional derivatives; electrical circuits; fractional differential equations

Citation: Ndolane Sene. Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives. AIMS Mathematics, 2019, 4(1): 147-165. doi: 10.3934/Math.2019.1.147


  • 1. Y. Adjabi, F. Jarad, T. Abdeljawad, On generalized fractional operators and a Gronwall type inequality with applications, Filomat, 31 (2017), 17.
  • 2. E. F. D. Goufo, Chaotic processes using the two-parameter derivative with non-singular and nonlocal kernel: Basic theory and applications, Chaos, 26 (2016), 084305.
  • 3. J. F. Gómez-Aguilar, Behavior characteristics of a cap-resistor, memcapacitor, and a memristor from the response obtained of RC and RL electrical circuits described by fractional differential equations, Turk. J. Elec. Eng. Comp. Sci., 24 (2016), 1421-1433.    
  • 4. J. F. Gómez-Aguilar, T. Cordova-Fraga, J. E. Escalante-Martínez, et al. Electrical circuits described by a fractional derivative with regular kernel, Rev. Mex. Fis., 62 (2016), 144-154.
  • 5. J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, V. H. Olivares-Peregrino, et al. Electrical circuits RC and RL involving fractional operators with bi-order, Adva. Mech. Eng., 9 (2017).
  • 6. J. F. Gómez-Aguilar, R. G. Juan, G. C. Manuel, et al. Fractional RC and LC electrical circuits, Ing., Invest. Tecno., 15 (2014), 311-319.
  • 7. J. F. Gómez-Aguilar, J. Rosales-García, R. F. Escobar-Jiménez, et al. On the possibility of the jerk derivative in electrical circuits, Adv. Math. Phys., 2016 (2016), 9740410.
  • 8. J. F. Gómez-Aguilar, V. F. Morales-Delgado, M. A. Taneco-Hernández, et al. Analytical solutions of the electrical RLC circuit via Liouville-Caputo operators with local and non-local kernels, Entropy,18 (2016), 402.
  • 9. F. Jarad, T. Abdeljawad, A modified Laplace transform for certain generalized fractional operators, Results Nonlinear Anal., 2018 (2018), 88-98.
  • 10. V. F. Morales-Delgado, J. F. Gómez-Aguilar, M. A. Taneco-Hernandez, Analytical solutions of electrical circuits described by fractional conformable derivatives in Liouville-Caputo sense, AEU-Int. J. Electron. C., 85 (2018), 108-117.    
  • 11. M. A. Moreles, R. Lainez, Mathematical modelling of fractional order circuits, (2016).
  • 12. S. Priyadharsini, Stability of fractional neutral and integrodifferential systems, J. Fract. Calc. Appl., 7 (2016), 87-102. 165
  • 13. D. Qian, C. Li, R. P. Agarwal, et al. Stability analysis of fractional differential system with Riemann-Liouville derivative, Math. Comp. Model., 52 (2010), 862-874.    
  • 14. A. G. Radwan, A. S. Elwakil, A. M. Soliman, On the generalization of second-order filters to the fractional-order domain, J. Circuit. Syst. Comp., 18 (2009), 361-386.    
  • 15. A. G. Radwan, K. N. Salama, Fractional-order RC and RL circuits, Circuits, Syst., Signal Process., 31 (2012), 1901-1915.    
  • 16. N. Sene, Exponential form for Lyapunov function and stability analysis of the fractional differential equations, J. Math. Computer Sci.,18 (2018), 388-397.    
  • 17. N. Sene, Lyapunov characterization of the fractional nonlinear systems with exogenous input, Fractal. Fract., 2 (2018).
  • 18. N. Sene, Fractional input stability and its application to neural network, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), in press.
  • 19. N. Sene, Mittag-Leffler input stability of fractional differential equations and its applications, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), in press.
  • 20. P.V. Shah, A. D. Patel, I. A. Salehbhai, et al. Analytic solution for the RL electric circuit model in fractional order, In Abst. Appli. Analy., 2014 (2014), 343814.
  • 21. R. Zhang, G. Tian, S. Yang, et al. Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2), ISA T., 56 (2015), 102-110.    


This article has been cited by

  • 1. Ndolane Sene, Gautam Srivastava, Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations, Symmetry, 2019, 11, 5, 608, 10.3390/sym11050608
  • 2. Ndolane Sene, José Francisco Gómez Aguilar, Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives, Fractal and Fractional, 2019, 3, 3, 39, 10.3390/fractalfract3030039
  • 3. Ndolane Sene, Stability analysis of electrical RLC circuit described by the Caputo-Liouville generalized fractional derivative, Alexandria Engineering Journal, 2020, 10.1016/j.aej.2020.01.008

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