Analytic and numerical solutions of discrete Bagley–Torvik equation.

In this research article, a discrete version of the fractional Bagley–Torvik equation is proposed: 1 ∇ h 2 u (t) + A C ∇ h ν u (t) + B u (t) = f (t) , t > 0 , where 0 < ν < 1 or 1 < ν < 2 , subject to u (0) = a and ∇ 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. [ABSTRACT FROM AUTHOR]