Analytical Formulation of Higher-Order q-Difference and Alpha q-Difference Equations with Two Parameters.

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Bibliographic Details
Title:	Analytical Formulation of Higher-Order q-Difference and Alpha q-Difference Equations with Two Parameters.
Authors:	S., Divya Bharathi¹ divyabharathitacw@gmail.com, T. G., Gerly² gerly@shctpt.edu
Source:	IAENG International Journal of Applied Mathematics. Jul2026, Vol. 56 Issue 7, p2524-2535. 12p.
Subjects:	Difference operators, Difference equations, Identities (Mathematics), Dynamical systems, Mathematical notation
Abstract:	This paper develops a generalized higher-order anti-q-difference operator for functions of two real variables ι and, extended to an γ-scaled q-difference equation with a product representation. The framework generalizes inverse q-difference operators to arbitrary order via a unified finite summation structure with r(k)-weighted coefficients. Recursive and closed-form identities among 1 q, 2 q, and 3 q are established. The α-parameter enhances flexibility for modeling geometrically scaled discrete systems, and a product form reveals intrinsic multiplicative structures. Special cases, including ι=γ, yield simplified expressions, while reductions recover classical operators. Numerical results confirm consistency and computational stability. The approach provides a foundation for two-variable q-difference equations and related discrete dynamical models. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This paper develops a generalized higher-order anti-q-difference operator for functions of two real variables ι and, extended to an γ-scaled q-difference equation with a product representation. The framework generalizes inverse q-difference operators to arbitrary order via a unified finite summation structure with r(k)-weighted coefficients. Recursive and closed-form identities among 1 q, 2 q, and 3 q are established. The α-parameter enhances flexibility for modeling geometrically scaled discrete systems, and a product form reveals intrinsic multiplicative structures. Special cases, including ι=γ, yield simplified expressions, while reductions recover classical operators. Numerical results confirm consistency and computational stability. The approach provides a foundation for two-variable q-difference equations and related discrete dynamical models. [ABSTRACT FROM AUTHOR]
ISSN:	19929978