Existence Of Solutions For The Boundary Value Problem Of Fractional Differential Equations

In this paper, we mainly study the existence and uniqueness of solutions and pos-itive solutions for boundary value problem of fractional differential equations involving Caputo derivative.First, we study the existence of solutions for the following boundary value problem of fractional differential equations: (?) where 1<α< 2,0≤λ<1/8, cDαis Caputo fractional derivative, and f:[0,1]×R→R is continuous. Under several types of sufficient conditions, the existence of solutions for the above problem is proved by fixed-point theorems.Furthermore, we discuss another type of boundary value problem for fractional order differential equations as follows: (?) where the fractional derivative operator cDαis also taken in the Caputo sense, and a∈(n-1, n], n∈N, n≥2.0<β< 1,f:[0,1]×R×R→R is continuous, h:R→R is continuous.