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In this article, we study the existence and uniqueness of solutions for system of fractional hybrid differential equations of order n−1 < ν ≤ n, without compactness of operator for the given toppled system  Dν(x(t)−Θ(t,x(t)) = Φ(t,y(t), Iν y(t)), Dν(y(t)−Θ(t,y(t)) = Φ(t,x(t), Iν x(t)),a.e t ∈ θ , n−1 ≤ ν < n, x(0) = x ′ (0) = x ′′ (0) = · · ·= xn−2(0) = 0, x(1) = ψ(x(η)), y(0) = y ′ (0) = y ′′ (0) = · · ·= yn−2(0) = 0, y(1) = φ(y(ζ )),0 < η ,ζ < 1 (0.1) where ψ,φ : [0,1] → R linear and Dν is the R-L fractional derivative of order ν , θ = [0,1], and the functions Θ : θ ×R → [0,1], Θ(0,0) = 0, and Φ : θ ×R×R → [0,1] are continuous and satisfy certain conditions. We established sufficient conditions for the existence and uniqueness of solutions using fixed point theorem on topological degree method. We provide an example to justify the obtained results.

Existence and uniqueness of solutions for coupled system of fractional differential equation by means of topological degree method