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In the current study, we introduce the two-variable analogue of Jacobi matrix polynomials. Some properties of these polynomials such as generating matrix functions, a Rodrigue-type formula and recurrence relations are also derived. Furthermore, some relationships and applications are reported.

The aim of this work is to introduce two families, BΣ(P;ϑ) and OΣ(X;ϑ), of holomorphic and bi-univalent functions involving the Bazilevič functions and the Ozaki-close-to-convex functions, by using generalized telephone numbers. We determinate upper bounds on the Fekete-Szegö type inequalities and the initial Taylor-Maclaurin coefficients for functions in these families. We also highlight certain edge cases and implications for our findings. [ABSTRACT FROM AUTHOR]

In this manuscript, we present a new definition of $ (k,\tau) $ (k , τ) -Gauss hypergeometric matrix function and study its analytical properties, like derivative formulas and integral representations. Furthermore, as an application we establish $ {\rm k} $ k -fractional calculus operators for the novel matrix function. We also give some new and known results as special cases of our proposed generalization of the Wright hypergeometric matrix function. [ABSTRACT FROM AUTHOR]

In this work, we define an extension of the k-Wright ((k;τ)-Gauss) hypergeometric matrix function and obtain certain properties of this function. Further, we present this function to achieve the solution of the fractional kinetic equations. [ABSTRACT FROM AUTHOR]