An application of s-elementary wavelets in numerical solution of differential and fractional integral equations - Mohammad Javad Kheirdeh; Ataollah Askari Hemmat; Habibollah Saeedi (Journal of Mahani Mathematical Research)
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 $α >0$, 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.