Open Journal Systems

A new approach for solving fractional RL circuit model through quadratic Legendre multi-wavelets

Narottam Singh Chauhan

Article ID: 724
Vol 1, Issue 1, 2018, Article identifier:

VIEWS - 461 (Abstract) 319 (PDF)


The aim of present work is to obtain the approximate solution of fractional model for the electrical RL circuit by using quadratic Legendre multiwavelet method (QLMWM). The beauty of the paper is convergence theorem and mean square error analysis, which shows that our approximate solution converges very rapidly to the exact solution and the numerical solution is compared with the classical solution and Legendre wavelets method (LWM) solution, which is much closer to the exact solution. The fractional integration is described in the Riemann-Liouville sense. The results are shows that the method is very effective and simple. In addition, using plotting tools, we compare approximate solutions of each equation with its classical solution and LWM .


Electrical circuit, Fractional differential equation, Quadratic Legendre multiwavelet

Full Text:


Included Database


Razzaghi, M., Yousefi, S.: Legendre wavelet direct method for variational problems, Math. Comput. Simulat. 53, 185-192 (2000)

Razzaghi, M., Yousefi, S.: Legendre wavelet method for constrained optimal control problems, Math. Method Appl. Sci. 25, 529-539 (2002)

Jafari, H., Yousefi, S., Firoozjaee, M., Momani, S., Khalique, C.M.: Application of Legendre wavelets for solving fractional differential equations, Comp. and Math. with Appl. 62, 1038-1045 (2011)

Wang, Y., Fan, Q.: The second kind chebyshev wavelet method for solving fractional differential equations, Appl. Math. and Comput. 218, 8592-8601 (2012)

Heydari, M.H., Hooshmandasl, M.R., Mohummadi, F.: Legendre wavelets method for solving fractional partial differential equations with Dirichlet boundary conditions, Appl. Math. and comput. 234, 267-276 (2014)

Rehman, M., Khan R.A.: The Legendre wavelets method for solving fractional differential equations, Commun. Nonlinear Sci. Numer. Simulat. 16, 4163-4173 (2011)

Oldham, K.B., Spanier, J.: The fractional calculus. Academic Press, New York (1974)

Miller, K.S., Ross, B.: An introduction to the Fractional calculus and fractional differential equations, Wiley New York (1993)

Podlubny, I.: Fractional differential equations, Academic Press, New York (1999)

Chen, J.: Analysis of stability and convergence of numerical approximation for the riesz functional reaction-dispersion equation, J. Xiamen Univ. Nat. Sci. 46, 616-619 (2007)

Liu, F., Anh, V., Turner, I.: Numerical solution of the space fractional Fokker-Planck equation, J. Comput. Appl. Math. 166, 209-219 (2004)

Chen, S., Liu, F.: Finite difference approximations for the fractional Fokker Planck equation, Appl. Math. Modell. 33, 256-273 (2009)

He, J.: Nonlinear oscillation with fractional derivative and its applications, Int. Conf. Vibr. Eng. 98, 288-291 (1998)

Mairardi, F.: Fractional calculus- Some basic problems in continuum and statistical mechanics, Fract. Calculus Conth. Mech. pp. 291-348 Springer (1997)

He, J.: Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol. 15, 86-90 (1999)

Bohannan, G.: Analogy fractional order controller in temperature and motor control applications, J. Vibr.

Control. 14, 1487-1498 (2008)

Panda, R., Dash, M.: Fractional generalized splines and signal processing, Signal Pro. 86, 2340-2350 (2006)

Chow, T.: Fractional dynamics of interfaces between soft-nanoparticales and rough substrates, Phys. Lett. A. 342, 148-155 (2005)

Gomez, F., Rosales, J., Guia, M.: RLC electrical circuit of non-integer order, Cent. Europ. J. of Phy. 11, 1361-1365 (2013)

Atangana, A. and Nieto, J.J.: Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel, Adv. Mech. Eng. (2015). doi: 10.1177/168714015613758

Alsaedi, A., Nieto, J., Venktesh, V.: Fractional electrical circuits, adv. in mech. eng. 7, 1-7 (2015)

Abbas, S., Benchohra, M., N’Guerekata, G.M.: Topics in fractional differential equations. Springer, New York (2012)

Diethelm, K.: The analysis of fractional differential equations- An application-oriented exposition using differential operators of caputo type, 2004 (Lecture notes in Mathematics), Springer-Verlag, Berlin (2010)

L. Debnath, “Wavelet Transforms and Their Applications” Birkhauser, Boston, (2002)

Chui, C.K.: Wavelets- A mathematical tool for signal analysis, SIAM, Philadelphia PA (1997)

Strela, V.: Multiwavelets Theory and application, Ph.D. Thesis, MIT University (1996)

Pathak, A.: Numerical solution of linear integro-differential equation by using quadratic Legendre multiwavelets direct method, J. of Adva. Res. in Sci. Comput. 4, 1-11 (2012)

Arora, R., Chauhan, N.S.: An efficient decomposition method for solving telegraph equation through quadratic legendre multiwavelets, Int. J. Of Appl. And Comput. Math. (2016). doi: 10.1007/s40819-016-0178-3

M. H. Heydari, M. R. Hooshmandasl, F. M. M. Ghaini, F. Mohummadi, Wavelet collocation method for solving multi order fractional differential equations, J. Appl. Math. (2012). doi: 10.1155/2012/542401

Alpert, B.: A class of bases in for the sparse representation of integration operator, SIAM J. Math. Anal. 24, 246-262 (1993)

Daubechies, I.: Ten Lectures on Wavelet, SIAM, Philadelphian (1992)

(461 Abstract Views, 319 PDF Downloads)


  • There are currently no refbacks.

Copyright (c) 2018 Narottam Singh Chauhan

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.