Computational Methods for Differential Equations Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary condi-tions

Parisa Rahimkhani, Yadollah Ordokhani, Esmail Babolian
2017 unpublished
In this manuscript a new method is introduced for solving fractional differential equations. The fractional derivative is described in the Caputo sense. The main idea is to use fractional-order Legendre wavelets and operational matrix of fractional-order integration. First the fractional-order Legendre wavelets (FLWs) are presented. Then a family of piecewise functions is proposed, based on which the fractional order integration of FLWs are easy to calculate. The approach is used this
more » ... l matrix with the collocation points to reduce the under study problem to a system of algebraic equations. Convergence of the fractional-order Legendre wavelet basis is demonstrate. Illustrative examples are included to demonstrate the validity and applicability of the technique.