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# Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method

by 3,* and
1
School of Natural Sciences, National University of Sciences and Technology, Islamabad 44000, Pakistan
2
NUST Institute of Civil Engineering, School of Civil and Environmental Engineering, National University of Sciences and Technology, Islamabad 44000, Pakistan
3
Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1164; https://doi.org/10.3390/math7121164
Received: 21 September 2019 / Revised: 8 November 2019 / Accepted: 11 November 2019 / Published: 2 December 2019
(This article belongs to the Special Issue Computational Methods in Applied Analysis and Mathematical Modeling)
In this study, we present a novel numerical scheme for the approximate solutions of linear as well as non-linear ordinary differential equations of fractional order with boundary conditions. This method combines Cosine and Sine (CAS) wavelets together with Green function, called Green-CAS method. The method simplifies the existing CAS wavelet method and does not require conventional operational matrices of integration for certain cases. Quasilinearization technique is used to transform non-linear fractional differential equations to linear equations and then Green-CAS method is applied. Furthermore, the proposed method has also been analyzed for convergence, particularly in the context of error analysis. Sufficient conditions for the existence of unique solutions are established for the boundary value problem under consideration. Moreover, to elaborate the effectiveness and accuracy of the proposed method, results of essential numerical applications have also been documented in graphical as well as tabular form. View Full-Text
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MDPI and ACS Style

Ismail, M.; Saeed, U.; Alzabut, J.; ur Rehman, M. Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method. Mathematics 2019, 7, 1164. https://doi.org/10.3390/math7121164

AMA Style

Ismail M, Saeed U, Alzabut J, ur Rehman M. Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method. Mathematics. 2019; 7(12):1164. https://doi.org/10.3390/math7121164

Chicago/Turabian Style

Ismail, Muhammad; Saeed, Umer; Alzabut, Jehad; ur Rehman, Mujeeb. 2019. "Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method" Mathematics 7, no. 12: 1164. https://doi.org/10.3390/math7121164

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