2 research outputs found
Sinc-Galerkin method for approximate solutions of fractional order boundary value problems
Sinc-Galerkin method for approximate solutions of fractional order boundary value problems
In this paper we present an approximate solution of a fractional order
two-point boundary value problem (FBVP). We use the sinc-Galerkin method
that has almost not been employed for the fractional order differential
equations. We expand the solution function in a finite series in terms
of composite translated sinc functions and some unknown coefficients.
These coefficients are determined by writing the original FBVP as a
bilinear form with respect to some base functions. The bilinear forms
are expressed by some appropriate integrals. These integrals are
approximately solved by sinc quadrature rule where a conformal map and
its inverse are evaluated at sinc grid points. Obtained results are
presented as two new theorems. In order to illustrate the applicability
and accuracy of the present method, the method is applied to some
specific examples, and simulations of the approximate solutions are
provided. The results are compared with the ones obtained by the Cubic
splines. Because there are only a few studies regarding the application
of sinc-type methods to fractional order differential equations, this
study is going to be a totally new contribution and highly useful for
the researchers in fractional calculus area of scientific research