diff --git a/examples/Brusselator.jl b/examples/Brusselator.jl
index 4288bd2a..77f3b1b8 100644
--- a/examples/Brusselator.jl
+++ b/examples/Brusselator.jl
@@ -10,7 +10,7 @@ function Brusselator!(du, u, p, t)
     du[2] = μ*u[1]-(u[1])^2*u[1]
 end
 
-prob = FODESystem(Brusselator!, α, u0, 100)
+prob = FODESystem(Brusselator!, α, u0, (0, 100))
 result = solve(prob, h, GL())
 
 # Phase plane
diff --git a/src/FractionalDiffEq.jl b/src/FractionalDiffEq.jl
index e0ffe651..6e6c9a98 100644
--- a/src/FractionalDiffEq.jl
+++ b/src/FractionalDiffEq.jl
@@ -19,7 +19,7 @@ include("singletermfode/PECE.jl")
 include("singletermfode/PI.jl")
 include("singletermfode/GL.jl")
 include("singletermfode/ChebSpectral.jl")
-include("singletermfode/AS.jl")
+include("singletermfode/AtanganaSeda.jl")
 
 # Multi-terms fractional ordinary differential equations
 include("multitermsfode/matrix.jl")
diff --git a/src/singletermfode/AS.jl b/src/singletermfode/AtanganaSeda.jl
similarity index 100%
rename from src/singletermfode/AS.jl
rename to src/singletermfode/AtanganaSeda.jl
diff --git a/src/singletermfode/PECE.jl b/src/singletermfode/PECE.jl
index 26bc6be9..d3e21a71 100644
--- a/src/singletermfode/PECE.jl
+++ b/src/singletermfode/PECE.jl
@@ -36,7 +36,7 @@ Define a single term fractional ordinary differential equation, there are only o
 struct SingleTermFODEProblem <: FDEProblem
     f::Function
     α::Float64
-    u0
+    u0::Union{AbstractArray, Number}
     tspan::Union{Tuple, Number}
 end
 
@@ -85,7 +85,7 @@ Construct system of fractional delay differential equations problem.
 struct FDDESystem <: FDEProblem
     f::Function
     ϕ::AbstractArray
-    α
+    α::Union{AbstractArray, Number}
     τ::Number
     T
 end
@@ -265,7 +265,7 @@ function right(f, y, α, n, h::Float64)
     return temp
 end
 
-function predictor(f, y, α::Float64, n::Integer, h::Float64, u0, t0)
+function predictor(f::Function, y, α::Float64, n::Integer, h::Float64, u0, t0)
     predict = 0
     leftsum = 0