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Computational Methods for Differential Equations Fractional-order Legendre wavelets and their applications for solving fractional-order differential equations with initial/boundary condi-tions
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 thisfatcat:hsywbc3iivbhxi3tkenvkvklou