Article

ANNALI DELL'UNIVERSITA' DI FERRARA

, 57:67

First online:

Approximation of fractional derivatives via Gauss integration

  • S. M. HashemiparastAffiliated withDepartment of Mathematics, Faculty of Science, K. N. Toosi University of Technology
  • , H. FallahgoulAffiliated withDepartment of Mathematics, Faculty of Science, K. N. Toosi University of Technology Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

This paper considers the approximations of three classes of fractional derivatives (FD) using modified Gauss integration (MGI) and Gauss-Laguerre integration (GLI). The main solutions of these fractional derivatives depend on the inverse of Laplace transforms, which are handled by these procedures. In the modified form of the integration, the weights and nodes are obtained by means of a difference equation that, gives a proper approximation form for the inverse of Laplace transform and hence the fractional derivatives. Theorems are established to indicate the degree of exactness and boundary of the error of the solutions. Numerical examples are given to illuminate the results of the application of these methods.

Keywords

Fractional derivative Laplace transform Gauss quadrature

Mathematics Subject Classification (2010)

26A33 44A10 41A55