Application of (q, Ï„)-Bernoulli Interpolation to the Spectral Solution of Quantum Differential Equations

Shaher Momani and Rabha W. Ibrahim

International Journal of Differential Equations, 2025, vol. 2025, 1-26

Abstract: In order to solve fractional differential equations on quantum domains, this work provides a spectral approach based on higher-order q,Ï„-Bernoulli functions and polynomials. We build a robust basis for approximation in q,Ï„-weighted Hilbert spaces by using the orthogonality properties of these extended polynomials and the Sheffer-type generating function. Prototype equations of the form Dq,Ï„ux=fx are numerically solved using the q,Ï„-Lagrange interpolation approach modified to represent arbitrary functions in terms of Bernoulli bases. Spectral expansion is used to recreate the solution, and a thorough example is given. The technique shows spectral convergence and shows how well higher-order q,Ï„-Bernoulli systems capture the global structure and local behavior of fractional quantum calculus solutions.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:4414882

DOI: 10.1155/ijde/4414882

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