On a Class of Difference Equations System of Fifth-Order

In the current paper, we investigate the following new class of system of difference equations {align} uₙ₊₁=&f⁻¹( g( vₙ₋₁) {A₁f( uₙ₋₂)+B₁g( vₙ₋₄) }{C₁f( uₙ₋₂)+D₁g( vₙ₋₄)}), \\ vₙ₊₁=&g⁻¹( f( uₙ₋₁) {A₂g( vₙ₋₂)+B₂f( uₙ₋₄) }{C₂g( vₙ₋₂)+D₂f( uₙ₋₄)}) ,\ n∈ N₀, {align} where the initial conditions u₋ₚ, v₋ₚ, for p=0,4̄ are real numbers, the parameters Aᵣ, Bᵣ, Cᵣ, Dᵣ, for r∈\1,2\ are real numbers, Aᵣ²+Bᵣ²≠ 0≠ Cᵣ²+Dᵣ², for r∈\1,2\, f and g are continuous and strictly monotone functions, f( R) =R, g( R) =R, f( 0) =0, g( 0) =0. In addition, we solve aforementioned general two dimensional system of difference equations of fifth-order in explicit form. Moreover, we obtain the solutions of mentioned system according to whether the parameters being zeros or not. Finally, we present an interesting application.