Chebyshev Wavelet Procedure for Solving FLDEs

Chebyshev Wavelet Procedure for Solving FLDEs Acta Appl Math https://doi.org/10.1007/s10440-018-0171-4 1,2 3 M.M. Khader · 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 1 Introduction 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Chebyshev Wavelet Procedure for Solving FLDEs

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Publisher
Springer Netherlands
Copyright
Copyright © 2018 by Springer Science+Business Media B.V., part of Springer Nature
Subject
Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
ISSN
0167-8019
eISSN
1572-9036
D.O.I.
10.1007/s10440-018-0171-4
Publisher site
See Article on Publisher Site

Abstract

Acta Appl Math https://doi.org/10.1007/s10440-018-0171-4 1,2 3 M.M. Khader · 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 1 Introduction 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

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Mar 16, 2018

References

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