Search

This article extends a numerical method for solving the fractional delay differential equations specified in terms of Caputo derivatives. The approach is based on the second kind Chebyshev wavelet. Our investigation is concentrated on convergence analysis and we prove a theorem for the error bound of the Chebyshev wavelets of the fractional differential in Caputo sense. Also, we discuss convergence analysis of the collocation method. In the end, some examples are presented to indicate the credibility and applicability of the numerical technique. The obtained results are compared with other numerical methods which our results are much more accurate than others. [ABSTRACT FROM AUTHOR]

Nowadays, the operational matrix plays an important role in solving problems with partial, ordinary or fractional derivatives. In the current study, we construct the operational matrix of the fractional integral for cubic B-spline scaling function and wavelets and it applies to solve va- rieties of the fractional integro-differential equations. To do this, firstly, the operational matrix of fractional integral for Haar scaling functions is constructed by using the definition of the Riemann-Liouville fractional integral operator and the orthogonal projection of polynomial on space of Haar scaling functions. Afterward, we obtain the operational matrix of cubic B-spline functions from fractional order using approximation cubic B-spline functions with Haar scaling functions and collocation method. The principal characteristics of this method are as follows: The opera- tional matrix of cubic B-spline functions is obtained simply because of the useful properties of the Haar scaling functions, reducing the time, the less occupation of the computer memory which converts to a system of linear and nonlinear equations. Finally, we will show the validity and efficiency of the new method by numerical examples and convergence analysis. [ABSTRACT FROM AUTHOR]