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Abstract In this paper, we consider a new fractional differential system on an unbounded domain Dαu(t)+φ(t,v(t),Dγ1v(t))=0,t∈[0,+∞),α∈(2,3],Dβv(t)+ψ(t,u(t),Dγ2u(t))=0,t∈[0,+∞),β∈(2,3], $$\begin{aligned} &D^{\alpha }u(t)+\varphi \bigl(t,v(t),D^{\gamma _{1}}v(t)\bigr)=0, \quad t \in [0,+ \infty ), \alpha \in (2,3], \\ &D^{\beta }v(t)+\psi \bigl(t,u(t),D^{\gamma _{2}}u(t)\bigr)=0, \quad t\in [0,+\infty ), \beta \in (2,3], \end{aligned}$$ subject to the conditions I3−αu(t)|t=0=0,Dα−2u(t)|t=0=∫0hg1(s)u(s)ds,Dα−1u(+∞)=Mu(ξ)+a,I3−βv(t)|t=0=0,Dβ−2v(t)|t=0=∫0hg2(s)v(s)ds,Dβ−1v(+∞)=Nv(η)+b. $$\begin{aligned} &I^{3-\alpha }u(t)|_{t=0}=0, \quad\quad D^{\alpha -2}u(t)|_{t=0}= \int _{0}^{h} g _{1}(s)u(s)\,ds, \quad \quad D^{\alpha -1}u(+\infty )=Mu(\xi )+a, \\ &I^{3-\beta }v(t)|_{t=0}=0, \quad\quad D^{\beta -2}v(t)|_{t=0}= \int _{0}^{h} g _{2}(s)v(s)\,ds, \quad \quad D^{\beta -1}v(+\infty )=Nv(\eta )+b. \end{aligned}$$ The nonlinear terms φ and ψ are dependent on the fractional derivative of lower order γi∈(0,1) $\gamma _{i}\in (0,1)$, i=1,2 $i=1,2$, which creates additional complexity to verify the existence of solutions. Moreover, a proper choice of Banach space allows the solutions to be defined on the half-line. From some standard fixed point theorems, sufficient conditions for the existence and uniqueness of solutions to boundary value problems are developed. Finally, the main result is applied to an illustrative example.