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Sequential fractional differential equations with three-point boundary conditions. (English) Zbl 1268.34006
Summary: We study a nonlinear three-point boundary value problem of sequential fractional differential equations of order $\alpha +1$ with $1<\alpha \le 2$. The expression for Green’s function of the associated problem involving the classical gamma function and the generalized incomplete gamma function is obtained. Some existence results are obtained by means of Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. An illustrative example is also presented. Existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results.
##### MSC:
 34A08 Fractional differential equations 34B10 Nonlocal and multipoint boundary value problems for ODE