Solving nonlinear Volterra integro-differential equations of fractional order by using Euler wavelet method
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- 作者：Yanxin Wang ; Li Zhu
- 关键词：Volterra integro ; differential equations ; Euler wavelet ; operational matrix ; Caputo derivative ; numerical solution
- 刊名：Advances in Difference Equations
- 出版年：2017
- 出版时间：December 2017
- 年：2017
- 卷：2017
- 期：1
- 全文大小：1432KB
- 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
- 出版者：Springer International Publishing
- ISSN：1687-1847
- 卷排序：2017
文摘
In this paper, a wavelet numerical method for solving nonlinear Volterra integro-differential equations of fractional order is presented. The method is based upon Euler wavelet approximations. The Euler wavelet is first presented and an operational matrix of fractional-order integration is derived. By using the operational matrix, the nonlinear fractional integro-differential equations are reduced to a system of algebraic equations which is solved through known numerical algorithms. Also, various types of solutions, with smooth, non-smooth, and even singular behavior have been considered. Illustrative examples are included to demonstrate the validity and applicability of the technique.