On Nonlocal Boundary Value Problems for Nonlinear Integro-differential Equations of Arbitrary Fractional Order

摘要

In this paper, we prove the existence of solutions of a nonlocal boundary value problem for nonlinear integro-differential equations of fractional order given by where q ∈(m-1,m],m ∈ ?, m ≥ 2, 0 < η < 1, and φxand ψx are integral operators. The existence results are established by means of the contraction mapping principle and Krasnoselskii's fixed point theorem. An illustrative example is also presented.