A new approach for solving fractional RL circuit model through quadratic Legendre multi-wavelets
Vol 1, Issue 1, 2018, Article identifier:
VIEWS - 461 (Abstract) 319 (PDF)
Abstract
Keywords
Full Text:
PDFReferences
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)
DOI: http://dx.doi.org/10.18063/ijmp.v1i1.724
(461 Abstract Views, 319 PDF Downloads)
Refbacks
- There are currently no refbacks.
Copyright (c) 2018 Narottam Singh Chauhan

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