A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices
Communications on Applied Nonlinear Analysis
This paper is devoted to a study of a nonlocal boundary value problem for a nonlinear differential equation depending on two fractional orders α,β∈(1,2]. The problem is inverted and an equivalent integral equation is constructed; as applications, the contraction mapping principle and a Krasnosel’skii fixed point theorem are applied to obtain sufficient conditions for the existence of solutions. An example illustrates the results. In the case that α=β=2, results for fourth order ordinary differential equations are obtained.
Ahmad, Bashir and Eloe, Paul, "A nonlocal boundary value problem for a nonlinear fractional differential equation with two indices" (2010). Mathematics Faculty Publications. 132.