Abstract by Aaron Larsen
Finite Difference Solution to the Bagley-Torvik Equation
Many definitions and fractional derivative operators are used in the study of fractional calculus in mathematics. A newly presented definition of the fractional derivative by R. Khali, et al. (2013) is analyzed using condition numbers and eigenvalues when using matrixes to solve ordinary differential equations. Numerical methods, specifically the finite difference method using boundary conditions, are applied to the Bagley-Torvik equation. This equation is used to describe the motion of a rigid plate in a Newtonian fluid. The results of using this new definition are then compared to those of the known fractional derivative operators of Riemann-Liouville and Caputo.