Abstract
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.