Existence results for \((n-1,1)\)-type nonlocal integral boundary value problems for coupled systems of fractional differential equations at resonance
Consider the boundary value problem \[ \begin{aligned} D^\alpha_{0+}u &= f(t,v,v',\dots, v^{(n-1)}),\quad 0<t<1,\\ D^\beta_{0+}v &= g(t,\breve u,\breve u',\dots, \breve u^{(n-1)}),\quad 0<t<1,\\ u^{(i)}(0) &= v^{(i)}(0)= 0\quad\text{for }0\leq i\leq n-2,\\ u(1) &= \lambda\int^\eta_0 u(t)\,dt,\quad v(1)= \mu\int^\xi_0 v(t)\,dt,\end{aligned}\tag{\(*\)} \] where \(n-1<\alpha\), \(\beta<n\), \(n\geq 2\), \(D^\alpha_{0+}\) and \(D^\beta_{0+}\) denote the Caputo fractional derivative, \(f,g:[0,1]\times \mathbb{R}^n\to\mathbb{R}\) are continuous functions, and \(\eta,\xi\in[0,1]\) are given constants satisfying \(\lambda\eta^n= \mu\xi^n=n\). The author studies \((*)\) by means of the coincidence theory.
scientific article; zbMATH DE number 6859487
scientific article