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In this paper, we investigate the existence and uniqueness of solutions for a differential equation of fractional-order q∈(1,2]$q \in(1, 2]$ subject to nonlocal boundary conditions involving Caputo derivative of the form x(0)=δx(σ),acDμx(ϱ1)+bcDμx(ϱ2)=c∫β1β2cDμx(s)ds,$$x(0)=\delta x(\sigma),\qquad a {}^{c}D^{\mu} x( \varrho_{1})+b {}^{c}D^{\mu} x(\varrho_{2})=c \int_{\beta_{1}}^{\beta_{2}} {}^{c}D^{\mu} x(s) \,ds, $$0<ϱ1<σ<β1<β2<ϱ2<1$0 < \varrho_{1} < \sigma< \beta_{1} < \beta_{2} < \varrho_{2} <1$, 0<μ<1$0<\mu<1$, and δ, a, b, c are real constants. We make use of some standard tools of fixed point theory to obtain the desired results which are well illustrated with the aid of examples.

Existence results for fractional-order differential equations with nonlocal multi-point-strip conditions involving Caputo derivative