%0 Journal Article %T An application of s-elementary wavelets in numerical solution of differential and fractional integral equations %J Journal of Mahani Mathematical Research %I Shahid Bahonar University of Kerman %Z 2251-7952 %A Kheirdeh, Mohammad Javad %A Askari Hemmat, Ataollah %A Saeedi, Habibollah %D 2022 %\ 11/01/2022 %V 11 %N 3 %P 15-31 %! An application of s-elementary wavelets in numerical solution of differential and fractional integral equations %K Integro-differential equations %K Fractional calculus %K Wavelet sets %K s-elementary wavelets %R 10.22103/jmmrc.2022.18821.1193 %X 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. %U https://jmmrc.uk.ac.ir/article_3260_40b44a8692c0c11f8133b6e1700c3008.pdf