INVESTIGATION OF THE BEHAVIOR OF THE FRACTIONAL BAGLEY TORVIK AND BASSET EQUATIONS VIA NUMERICAL INVERSE LAPLACE TRANSFORM
It is well known that the motion of a rigid plate floated in a Newtonian fluid and the unsteady motion of a sphere immersed in a Stokes fluid are described by equations involving derivative of real order. This work is devoted to the study of the fractional Bagley Torvik and Basset equations. Because of the difficulty of evaluating the inverse Laplace transforms for complicated non integer order differential equations, we investigate the validity of applying numerical inverse Laplace transform algorithms in fractional calculus. To this end, we introduce a method based on Gaussian quadrature formulae for numerical integration of the Bromwich's integral. We give a full presentation of the method and eventually show its efficiency and applicability through two illustrative examples.