The Triple Difference Operator of Binomial Poisson Matrix of Fractional

In this article we introduce binomial Poisson matrix difference sequence spaces of fractional order α, b_Γ³ʳˢ and b_Λ ³ʳˢ by employing fractional difference operator Δα defined by \[ Δα xₘₙₖ = ∑ᵤ₌₀∞ ∑ᵥ₌₀∞ ∑w=0∞ (-1)ᵘ⁺ᵛ⁺ʷ Γ(α+1)Γ(β+1)Γ(γ+1) / u!\,v!\,w!\, Γ(α-u+1) Γ(β-v+1) Γ(γ-w+1) xm-u,n-v,k-w. \] We give some topological properties, obtain the Schauder basis, and discuss various duals. Finally, we present a graphical interpretation of the operator Bʳˢ(Δα).