Nonlocal Integral Boundary Value Problem of Bagley-Torvik Type Fractional Differential Equations and Inclusions

摘要

In this article,we consider the Bagley-Torvik type fractional differential equation cDν1l(t)-acDν2l(t) =g(t,l(t)) and differential inclusion cDν1l(t)-acDν2l(t) ∈ G(t,l(t)),t ∈ (0,1) subjecting to l(0) =l0,and l(1) =λ'f0ω (ω-s)x-1t(s) / Γ(x) ds,where 1 ＜ ν1 ≤ 2,1 ≤ ν2 ＜ ν1,0 ＜ ω ≤ 1,x =ν1-ν2 ＞ 0,a,λ'are given constants.By using Leray-Schauder degree theory and fixed point theorems,we prove the existence of solutions.Our results extend the existence theorems for the classical Bagley-Torvik equation and some related models.