An integro quadratic spline approach for a class of variable-order fractional initial value problems

This paper develops a technique for the approximate solution of a class of variable-order fractional differential equations useful in the area of fluid dynamics. The method adopts a piecewise integro quadratic spline interpolation and is used in the study of the variable-order fractional Bagley-Torvik and Basset equations. The accuracy of the proposed algorithm is verified by means of illustrative examples.