Lekesiz, Esra GuldoganCekim, BayramOzarslan, Mehmet Ali2025-11-062025-11-0620260377-04271879-1778https://doi.org/10.1016/j.cam.2025.117106https://hdl.handle.net/20.500.12416/15699Guldogan Lekesiz, Esra/0000-0001-7653-8745In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.eninfo:eu-repo/semantics/closedAccessFinite Biorthogonal PolynomialKonhauser PolynomialMittag-Leffler FunctionFractional OperatorLaplace TransformFourier TransformArticle10.1016/j.cam.2025.1171062-s2.0-105017634579