1. Numerical methods (Spline functions, Finite difference, Finite element, Finite volume), analysis and computation.

In this paper, a new fractional spline method of non-polynomial form have been considered to solve special linear fractional
boundary-value problems. Using this fractional spline function a few consistency relations are derived for computing approximations
to the solution of the problem. Convergence analysis and error estimates of this methods are discussed. Numerical results are provided
to demonstrate the superiority of our methods.