A NEW OPERATIONAL MATRIX APPROACH BASED ON LEGENDRE WAVELETS FOR FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

This present paper suggests a new numerical algorithm to solve fractional differential equations (FDEs) based upon a Legendre wavelet operational matrix of fractional integration (LW-OMFI). The strategy is efficient in converting original FDEs such as Caputo and Riemann-Liouville derivation into a set of algebraic equations. With its ability to take advantage of the orthogonality and compact support of Legendre wavelets, spreading out the Galerkin expansion over a large number of higher frequency basis function elements is made good, as well as minimizing the number of required elements. The operational matrix is deduced systematically in order to treat fractional integrals so that it is possible to treat both linear and nonlinear FDEs with it. Topical numerical tests prove the advantages of the new method over the traditional ones including the Adomian Decomposition Method (ADM) and Homotopy Analysis Method (HAM) in precision, convergence, and computational time. The method has especially good prospect of application in physics and engineering where fractional models are common.