Abstract
In this paper, new numerical method based on Chebyshev wavelet operational matrix of fractional derivative is presented. The known Chebyshev Wavelets is presented first. Then, we derived the operational matrix of fractional order derivative (OMOFOD), through wavelet transformation matrix which was utilized together with spectral and collocation methods to reduce the linear and nonlinear fractional differential equations (FDEs) to a system of algebraic equations respectively. Our results in solving different linear and nonlinear FDEs confirm the applicability and accuracy of the proposed method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kilbas, A., Aleksandrovich, A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations, vol. 204. Elsevier Science Limited (2006)
Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and Some of their Applications, vol. 198. Academic press (1998)
Ray, S.S., Chaudhuri, K.S., Bera, R. K.: Analytical approximate solution of nonlinear dynamic system containing fractional derivative by modified decomposition method. Appl. Math. Comput. 182(1) (2006)
Yang, S., Xiao, A., Su, H.: Convergence of the variational iteration method for solving multi-order fractional differential equations. Comput. Math. Appl. 60(10) (2010)
Odibat, Z.: On Legendre polynomial approximation with the VIM or HAM for numerical treatment of nonlinear fractional differential equations. J. Comput. Appl. Math. 235(9) (2011)
Li, Y., Zhao, W.: Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. Appl. Math. Comput. 216(8) (2010)
Jafari, H., et al.: Application of Legendre wavelets for solving fractional differential equations. Comput. Math. Appl. 62(3) (2011)
Yuanlu, L.: Solving a nonlinear fractional differential equation using Chebyshev wavelets. Commun. Nonlinear Sci. Numer. Simul. 15(9) (2010)
Keshavarz, E., Ordokhani, Y., Razzaghi, M.: Bernoulli wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations. Appl. Math. Model. 38(24) (2014)
Guf, J.-S., Jiang, W.-S.: The Haar wavelets operational matrix of integration. Int. J. Syst. Sci. 27(7) (1996)
Doha, E.H., Bhrawy, A.H., Ezz-Eldien, S.S.: A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. Comput. Math. Appl. 62(5) (2011)
El-Sayed, A.M.A., El-Mesiry, A.E.M., El-Saka, H.A.A.: Numerical solution for multi-term fractional (arbitrary) orders differential equations. Comput. Appl. Math. 23(1) (2004)
Acknowledgments
This work was supported in part by FRGS Grant Vot 1433. We also thank UTHM for financial support through GIPS U060.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Isah, A., Chang, P. (2017). Chebyshev Wavelet Operational Matrix of Fractional Derivative Through Wavelet-Polynomial Transformation and Its Applications on Fractional Order Differential Equations. In: Ahmad, AR., Kor, L., Ahmad, I., Idrus, Z. (eds) Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Springer, Singapore. https://doi.org/10.1007/978-981-10-2772-7_22
Download citation
DOI: https://doi.org/10.1007/978-981-10-2772-7_22
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-2770-3
Online ISBN: 978-981-10-2772-7
eBook Packages: EducationEducation (R0)