Abstract We study a fractional integro-differential equation subject to multi-point boundary conditions: D0+αu(t)+f(t,u(t),Tu(t),Su(t))=b, t∈(0,1),u(0)=u′(0)=⋯=u(n−2)(0)=0,D0+pu(t)|t=1=∑i=1maiD0+qu(t)|t=ξi, $$\left\{\begin{array}{l} D^\alpha_{0^+} u(t)+f(t,u(t),Tu(t),Su(t))=b,\ t\in(0,1),\\u(0)=u^\prime(0)=\cdots=u^{(n-2)}(0)=0,\\ D^p_{0^+}u(t)|_{t=1}=\sum\limits_{i=1}^m a_iD^q_{0^+}u(t)|_{t=\xi_i},\end{array}\right.$$ where α∈(n−1,n], n∈N, n≥3, ai≥0, 00 $\alpha\in (n-1,n],\ n\in \textbf{N},\ n\geq 3,\ a_i\geq 0,\ 0<\xi_1<\cdots<\xi_m\leq 1,\ p\in [1,n-2],\ q\in[0,p],b>0$. By utilizing a new fixed point theorem of increasing ψ−(h,r)− $\psi-(h,r)-$ concave operators defined on special sets in ordered spaces, we demonstrate existence and uniqueness of solutions for this problem. Besides, it is shown that an iterative sequence can be constructed to approximate the unique solution. Finally, the main result is illustrated with the aid of an example.

中文翻译：

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多点分数阶积分微分方程的唯一解

结果表明，可以构造一个迭代序列来逼近唯一解。最后，通过一个例子来说明主要结果。