Rift Valley fever is a zoonotic disease which is mainly transmitted by mosquitoes and has potential to affect humans and animals. To gain some understanding on its dynamics in an urban peridomestic cycle, a fractional-order derivative model is formulated and analysed. The basic reproduction number
ℛ
0
is computed and used in analysing the stability of disease when an outbreak occurs. Numerical simulations are performed in order to the variation of each population at order
α
=
1,0.75
,
0.5
, and 0.25. Results from simulations show that there is an increase in susceptible and exposed population in both human and mosquitoes as the value of
α
decreases. The infected population decreases with a decrease in the value of
α
. However, a rapid increase in susceptible mosquitoes is observed just after the first 30 days and a rapid decrease in infected human and mosquitoes after the first 30 days for
α
=
1
. Hence, fractional-order derivative also plays a significant role in providing insight on disease transmission and dynamics.