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A new operational matrix for solving fractional-order differential equations. (English) Zbl 1189.65151
Summary: Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equations. The fractional derivatives are described in the Caputo sense. Our main aim is to generalize the Legendre operational matrix to the fractional calculus. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
26A33Fractional derivatives and integrals (real functions)
34A08Fractional differential equations
45J05Integro-ordinary differential equations
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