MMN-3963
Bivariate k-Mittag-Leffler functions with 2D-k-Laguerre-Konhauser polynomials and corresponding k-fractional operators
Cemaliye Kürt; Mehmet Ali Özarslan;Abstract
In this paper, we first introduce new class of 2D-$k$-Laguerre-Konhauser polynomials, $_{\delta }L_{k,n}^{(\alpha ,\beta )}(x,y)$, which generalizes the 2D-Laguerre-Konhauser polynomials (see \cite{26a}). Then, we define a new family of bivariate \textit{k}-Mittag-Leffler functions $E_{k,\alpha ,\beta ,\delta }^{(\gamma )}(x,y)$ and establish the \textit{k}-Riemann-Liouville double fractional integral and derivative of the functions $E_{k,\alpha ,\beta ,\delta }^{(\gamma )}(x,y)$. Moreover, we introduce an integral operator $_{k}\varepsilon _{\alpha ,\beta ,\delta ;\omega _{1},\omega
_{2};a^{+},c^{+}}^{(\gamma )}$ which contains the bivariate $k$-Mittag-Leffler functions $E_{k,\alpha ,\beta ,\delta }^{(\gamma )}(x,y)$ in the kernel and investigate the semigroup property of this operator. Finally, the left inverse operator of the integral operator $_{k}\varepsilon _{\alpha ,\beta ,\delta ;\omega _{1},\omega
_{2};a^{+},c^{+}}^{(\gamma )}$ is constructed.
Vol. 24 (2023), No. 2, pp. 861-876