A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions

In this article, we discuss a new Hadamard fractional differential system with four-point boundary conditions [Formula: see text] where a, b are two parameters with 0 < ab(logη)α-1(logξ)β-1 < 1 , α, β ∈ (n - 1, n] are two real numbers and n ≥ 3 , f, g ∈ C([1, e] × ( - ∞,  + ∞), ( - ∞,  + ∞)) , lf, lg > 0 are constants, and DαH, HDβ are the Hadamard fractional derivatives of fractional order. Based upon a fixed point theorem of increasing φ- (h, r) -concave operators, we establish the existence and uniqueness of solutions for the problem dependent on two constants lf, lg .