Acta Appl Math
Chebyshev Wavelet Procedure for Solving FLDEs
· M. Adel
Received: 10 November 2017 / Accepted: 26 February 2018
© Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract We apply the operational matrices of fractional integration for Chebyshev
wavelets for solving the fractional (Caputo form) Logistic differential equation (FLDE).
We introduce a study of the convergence analysis and error estimation of the obtained ap-
proximation solution. The FLDE is reduced to a system of algebraic equations with the help
of the properties of wavelets polynomials. The numerical results conﬁrm the theoretical re-
sults and the efﬁciency of the proposed procedure. A numerical simulation and a comparison
with the previous work are presented. The proposed method can be applied to solve other
problems in engineering and physics.
Keywords Fractional LDE · Chebyshev wavelets · Convergence analysis
Mathematics Subject Classiﬁcation (2010) 41A30 · 65N12
Fractional differential equations (FDEs) have been the focus of many studies due to their fre-
quent appearance in various applications in ﬂuid mechanics, viscoelasticity, biology, physics
and engineering. Consequently, considerable attention has been given to the solutions of
FDEs. Since the exact solutions of these equations are not known so approximate and nu-
merical techniques [1, 3], must be used.
Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Department of Mathematics and Statistics, College of Science, Al Imam Mohammad Ibn Saud
Islamic University (IMSIU), Riyadh, Saudi Arabia
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt