Analytic and numerical solutions of discrete Bagley-Torvik equation

Abstract

In this research article, a discrete version of the fractional Bagley-Torvik equation is proposed:

del(2)(h)u(t) + A(C)del(nu)(h) u(t) + Bu(t) = f (t), t > 0, (1)

where 0 < nu < 1 or 1 < nu < 2, subject to u(0) = a and del(h)u(0) = b, with a and b being real numbers. The solutions are obtained by employing the nabla discrete Laplace transform. These solutions are expressed in terms of Mittag-Leffler functions with three parameters. These solutions are handled numerically for some examples with specific values of some parameters.