Existence of Positive Solutions for Multiterm Fractional Differential Equations of Finite Delay with Polynomial Coefficients

and Applied Analysis 3 Definition 2.2 see 15 . A cone K is called normal, if there exists a positive constant r such that f, g ∈ K and θ ≺ f ≺ g implies ‖f‖ ≤ r‖g‖, where θ denotes the zero element of K. Definition 2.3 see 16, 17 . Let f : a, b → R, and f ∈ L1 a, b . The left-sided RiemannLiouville fractional integral of f of order α is defined as I af x 1 Γ α ∫x a x − t α−1f t dt, α > 0, x ∈ a, b . 2.3 Definition 2.4 see 16, 17 . The left-sided Riemann-Liouville fractional derivative of a function f : a, b → R is defined as D af x D m[Im−α a f x ] , x ∈ a, b , 2.4 wherem α 1,D d/dt. We denoteD 0 byD α and I 0 by I . If the fractional derivative D af x is integrable, then 16, page 71 I a ( D β af x ) Iα−β a f x − [ I 1−β a f x ] x a xα−1 Γ α , 0 < β ≤ α < 1. 2.5 If f is continuous on a, b , then I1−β a f x x a 0 and 2.5 reduces to I a ( D β af x ) Iα−β a f x , 0 < β ≤ α < 1. 2.6 Proposition 2.5. Let y be continuous on 0, T , T > 0 and let n be a nonnegative integer, then