Abstract
In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann–Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the
Δ
2
, which will be useful to obtain the convexity results. We examine the correlation between the positivity of
(
w
0
RL
Δ
α
f
)
(
t
)
and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of
(
2
,
3
)
,
H
k
,
ϵ
and
M
k
,
ϵ
. The decrease of these sets allows us to obtain the relationship between the negative lower bound of
(
w
0
RL
Δ
α
f
)
(
t
)
and convexity of the function on a finite time set
N
w
0
P
:
=
{
w
0
,
w
0
+
1
,
w
0
+
2
,
…
,
P
}
for some
P
∈
N
w
0
:
=
{
w
0
,
w
0
+
1
,
w
0
+
2
,
…
}
. The numerical part of the paper is dedicated to examinin the validity of the sets
H
k
,
ϵ
and
M
k
,
ϵ
for different values of k and
ϵ
. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.