We analyze two implicit fractional linear multi-step methods of order four for solving fractional initial value problems. The methods are derived from the Grunwald-Letnikov approximation of fractional derivative at a non-integer shift point with super-convergence. The weight coefficients of the methods are computed fro …
We present and investigate a new type of implicit fractional linear multi-step method of order two for fractional initial value problems. The method is obtained from the second-order superconvergence of the Grünwald-Letnikov approximation of the fractional derivative at a non-integer shift point. The method coincides w …
We propose a generalized theory to construct higher order Grünwald type approximations for fractional derivatives. We use this generalization to simplify the proofs of orders for existing approximation forms for the fractional derivative. We also construct a set of higher order Grünwald type approximations for fraction …
In a recent paper (Nasir, 2007), a set of weakly orthogonal and completely orthogonal spherical harmonics in a non-polar spherical coordinate system based on a cubed-sphere was constructed. In this work, we explore some linear relations between these two sets of spherical harmonics. Moreover, a power representation for …