@article{Zayed2025, 
author = {Mohra Zayed and Waseem Ahmad Khan and Cheon Seoung Ryoo and Ugur Duran},
title = {An exploratory study on bivariate extended    q-Laguerre-based Appell polynomials with some applications},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {6},
pages = {12841-12867},
keywords = {quasi monomiality, extension of monomiality principle, quantum calculus, q-Laguerre polynomials, q-Dilatation operator, q-Laguerre-based Appell polynomials},
url = {https://www.sciopen.com/article/10.3934/math.2025577},
doi = {10.3934/math.2025577},
abstract = {In this paper, we employed the    q-Bessel Tricomi functions of zero-order to introduce bivariate extended    q-Laguerre-based Appell polynomials. Then, the bivariate extended    q-Laguerre-based Appell polynomials were established in the sense of quasi-monomiality. We examined some of their properties, such as    q-multiplicative operator property,    q-derivative operator property and two    q-integro-differential equations. Additionally, we acquired    q-differential equations and operational representations for the new polynomials. Moreover, we drew the zeros of the bivariate extended    q-Laguerre-based Bernoulli and Euler polynomials, forming 2D and 3D structures, and provided a table including approximate zeros of the bivariate extended    q-Laguerre-based Bernoulli and Euler polynomials.}
}