Ahmad, Bashir; Agarwal, Ravi P. On nonlocal fractional boundary value problems. (English) Zbl 1230.26003 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 18, No. 4, 535-544 (2011). Summary: We study a new class of non-local boundary value problems of nonlinear differential equations of fractional order. We extend the idea of a three-point non-local boundary condition \((x(1) = \alpha x(\eta ), \alpha \in \mathbb{R}, 0 < \eta < 1)\) to a non-local strip condition of the form: \(x(1) = \eta \int ^\tau _\nu x(s)ds, 0 < \nu < \tau < 1\). In fact, this strip condition corresponds to a continuous distribution of the values of the unknown function on an arbitrary finite segment of the interval. In the limit \(\nu \rightarrow 0, \tau \rightarrow 1\), this strip condition takes the form of a typical integral boundary condition. Some new existence and uniqueness results are obtained for this class of non-local problems by using standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also discussed. Cited in 25 Documents MSC: 26A33 Fractional derivatives and integrals 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable Keywords:fractional differential equations; nonlocal boundary conditions; fixed point theorems; Leray-Schauder degree PDFBibTeX XMLCite \textit{B. Ahmad} and \textit{R. P. Agarwal}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 18, No. 4, 535--544 (2011; Zbl 1230.26003) Full Text: Link