| Summary: | Abstract In this article, we discuss a new Hadamard fractional differential system with four-point boundary conditions {DαHu(t)+f(t,v(t))=lf,t∈(1,e),DβHv(t)+g(t,u(t))=lg,t∈(1,e),u(j)(1)=v(j)(1)=0,0≤j≤n−2,u(e)=av(ξ),v(e)=bu(η),ξ,η∈(1,e), $$\textstyle\begin{cases} {}^{H} D^{\alpha}u(t)+f(t,v(t))=l_{f},\quad t\in(1,e),\\ {}^{H} D^{\beta}v(t)+g(t,u(t))=l_{g},\quad t\in(1,e),\\ u^{(j)}(1)=v^{(j)}(1)=0, \quad 0\leq j\leq n-2,\\ u(e)=av(\xi),\qquad v(e)=bu(\eta),\quad \xi, \eta\in(1,e), \end{cases} $$ where a,b $a,b$ are two parameters with 0<ab(logη)α−1(logξ)β−1<1 $0< ab(\log\eta)^{\alpha-1}(\log\xi )^{\beta-1}<1$, α,β∈(n−1,n] $\alpha, \beta\in(n-1,n]$ are two real numbers and n≥3 $n\geq3$, f,g∈C([1,e]×(−∞,+∞),(−∞,+∞)) $f,g\in C([1,e]\times(-\infty,+\infty),(-\infty,+\infty))$, lf,lg>0 $l_{f}, l_{g}>0$ are constants, and DαH,HDβ ${}^{H} D^{\alpha}, {}^{H} D^{\beta}$ are the Hadamard fractional derivatives of fractional order. Based upon a fixed point theorem of increasing φ- (h,r) $(h,r)$-concave operators, we establish the existence and uniqueness of solutions for the problem dependent on two constants lf,lg $l_{f}, l_{g}$.
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