# An application of s-elementary wavelets in numerical solution of differential and fractional integral equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Payame Noor University (PNU) P. O. Box 19395-4697, Tehran, Iran

2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonal University of Kerman, Kerman, Iran.

3 Department of Applied Mathematics, Faculty of Mathematics and Computer & Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this article we introduce wavelet sets and consider a special wavelet set in R. We build a basis associated to this type wavelet sets and use operational matrix of this basis to solve nonlinear Riccati differential equations and Riemann-Liouville fractional integral equations of order $\alpha >0$, numerically. Convergence analysis of this basis is investigated. Also, we give examples that show the accuracy of the new method by comparing it with previous methods.

Keywords

#### References

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### History

• Receive Date: 07 January 2022
• Revise Date: 01 April 2022
• Accept Date: 18 April 2022
• First Publish Date: 18 April 2022