Fractional-order logistic differential equation with Mittag–Leffler-type Kernel

In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations of each solution in terms of a formal power series. Some numerical approximations are implemented by using truncated series.Agencia Estatal de Investigación | Ref. PID2020-113275GB-I00Xunta de Galicia | Ref. ED431C 2019/0

Some new families of finite orthogonal polynomials in two variables

In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family of univariate orthogonal polynomials. For these new classes of bivariate finite orthogonal polynomials, we present a bivariate weight function, the domain of orthogonality, the orthogonality relation, the recurrence relations, the second-order partial differential equations, the generating functions, as well as the parameter derivatives. The limit relations among these families are also presented in Labelle’s flavor.Agencia Estatal de Investigación | Ref. PID2020-113275GB-I00Scientific and Technological Research Council (Turquía) | Ref. 2218-122C24

Monic bivariate polynomials on quadratic and q-quadratic lattices

Monic families of bivariate Askey–Wilson polynomials and q-Racah polynomials are explicitly given. Monic families of bivariate orthogonal polynomials, both in quadratic and q-quadratic lattices, are also explicitly given using appropriate limit relations.Agencia Estatal de Investigación | Ref. MTM2016-75140-PAgencia Estatal de Investigación | Ref. PID2020-113275GB-I0