摘要：In this paper, we investigate the existence and uniqueness of solutions to the coupled system of nonlinear fractional differential equations { − D 0 + ν 1 y 1 ( t ) = λ 1 a 1 ( t ) f ( y 1 ( t ) , y 2 ( t ) ) , − D 0 + ν 2 y 2 ( t ) = λ 2 a 2 ( t ) g ( y 1 ( t ) , y 2 ( t ) ) , $$\left \{ \begin{array}{@{}l} -D^{\nu_)}_{0^{+}}y_)(t)=\lambda_)a_)(t)f(y_)(t),y_,(t)), \\ -D^{\nu_,}_{0^{+}}y_,(t)=\lambda_,a_,(t)g(y_)(t),y_,(t)), \end{array} \right . $$ where D 0 + ν $D^{\nu}_{0^{+}}$ is the standard Riemann-Liouville fractional derivative of order ν, t ∈ ( 0 , 1 ) $t\in(0,1)$ , ν 1 , ν 2 ∈ ( n − 1 , n ] $\nu_), \nu_, \in(n-1,n]$ for n > 3 $n>3$ and n ∈ N $n \in\mathbf{N} $ , and λ 1 , λ 2 > 0 $\lambda_), \lambda_, > 0$ , with the multi-point boundary value conditions: y 1 ( i ) ( 0 ) = 0 = y 2 ( i ) ( 0 ) $y^{(i)}_)(0)=0=y^{(i)}_,(0)$ , 0 ≤ i ≤ n − 2 $0 \leq i \leq n-2$ ; D 0 + β y 1 ( 1 ) = ∑ i = 1 m − 2 b i D 0 + β y 1 ( ξ i ) $D^{\beta}_{0^{+}}y_)(1)=\sum^{m-2}_{i=1}b_{i}D^{\beta }_{0^{+}}y_)(\xi_{i})$ ; D 0 + β y 2 ( 1 ) = ∑ i = 1 m − 2 b i D 0 + β y 2 ( ξ i ) $D^{\beta}_{0^{+}}y_,(1)=\sum^{m-2}_{i=1}b_{i}D^{\beta }_{0^{+}}y_,(\xi_{i})$ , where n − 2 < β < n − 1 $n-2 < \beta< n-1$ , 0 < ξ 1 < ξ 2 < ⋯ < ξ m − 2 < 1 $0 < \xi_) < \xi_, < \cdots< \xi_{m-2} <1$ , b i ≥ 0 $b_{i} \geq0$ ( i = 1 , 2 , … , m − 2 $i=1,2,\ldots,m-2$ ) with ρ 1 : = ∑ i = 1 m − 2 b i ξ i ν 1 − β − 1 < 1 $\rho_): = \sum^{m-2}_{i=1} b_{i}\xi^{\nu_)-\beta-1}_{i}<1$ , and ρ 2 : = ∑ i = 1 m − 2 b i ξ i ν 2 − β − 1 < 1 $\rho_,: =\sum^{m-2}_{i=1} b_{i}\xi^{\nu_,-\beta-1}_{i}<1$ . Our analysis relies on the Banach contraction principle and Krasnoselskii’s fixed point theorem.
关键词：existence and uniqueness ; solutions ; Riemann-Liouville fractional derivative ; multi-point boundary value problems ; Banach contraction principle ; Krasnoselskii’s fixed point theorem
