The Triple Difference Operator of Binomial Poisson Matrix of Fractional

Key Points

• The aim is to introduce new difference sequence spaces using a fractional difference operator associating to binomial Poisson matrices.
• Defined a fractional difference operator $\Delta^{\alpha}$ with a specific series involving Gamma functions.
• Explored topological properties of the defined sequence spaces $b_{\Gamma^{3}}^{rs}$ and $b_{\Lambda^{3}}^{rs}$.
• Obtained the Schauder basis and discussed its various duals.
• Presented a graphical interpretation of the operator $B^{rs}(\Delta^{\alpha})$.
• Introduced the mathematical structure of fractional order for difference sequence spaces.
• Established the existence of a Schauder basis for these spaces.
• Provided graphical insights into the operation of the defined fractional difference operator.