Positive Solutions for Fractional Differential Equations from Real Estate Asset Securitization via New Fixed Point Theorem

and Applied Analysis 3 Remark 2.3. If x, y : 0, ∞ → R with order α > 0, then Dt ( x t y t ) Dtx t Dty t . 2.3 Proposition 2.4 see 18, 19 . 1 If x ∈ L1 0, 1 , ν > σ > 0, then IIx t I x t , DtIx t Iν−σx t , DtIx t x t . 2.4 2 If ν > 0, σ > 0, then Dttσ−1 Γ σ Γ σ − ν t σ−ν−1. 2.5 Proposition 2.5 see 18, 19 . Let α > 0, and f x is integrable, then IDtf x f x c1xα−1 c2xα−2 · · · cnxα−n, 2.6 where ci ∈ R (i 1, 2, . . . , n), n is the smallest integer greater than or equal to α. Let x t Iy t , y t ∈ C 0, 1 , by standard discuss, we easily reduce the BVP 1.1 to the following modified problems: −Dty t f ( t, Iy t ,−y t ) , y 0 y′ 0 0, y 1 ∫1