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

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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]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Analytical Formulation of Higher-Order q-Difference and Alpha q-Difference Equations with Two Parameters.
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  Data: <searchLink fieldCode="AR" term="%22S%2E%2C+Divya+Bharathi%22">S., Divya Bharathi</searchLink><relatesTo>1</relatesTo><i> divyabharathitacw@gmail.com</i><br /><searchLink fieldCode="AR" term="%22T%2E+G%2E%2C+Gerly%22">T. G., Gerly</searchLink><relatesTo>2</relatesTo><i> gerly@shctpt.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2026, Vol. 56 Issue 7, p2524-2535. 12p.
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  Data: <searchLink fieldCode="DE" term="%22Difference+operators%22">Difference operators</searchLink><br /><searchLink fieldCode="DE" term="%22Difference+equations%22">Difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Identities+%28Mathematics%29%22">Identities (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+notation%22">Mathematical notation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 12
        StartPage: 2524
    Subjects:
      – SubjectFull: Difference operators
        Type: general
      – SubjectFull: Difference equations
        Type: general
      – SubjectFull: Identities (Mathematics)
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      – SubjectFull: Dynamical systems
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      – SubjectFull: Mathematical notation
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      – TitleFull: Analytical Formulation of Higher-Order q-Difference and Alpha q-Difference Equations with Two Parameters.
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              Text: Jul2026
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              Y: 2026
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