Corrigendum to “Identities involving Frobenius–Euler polynomials arising from non-linear differential equations” [J. Number Theory 132 (12) (2012) 2854–2865]

Some identities of degenerate Fubini polynomials arising from differential equations

Recently, Kim et al. have studied degenerate Fubini polynomials in [T. Kim, D. V. Dolgy, D. S. Kim, J. J. Seo, J. Nonlinear Sci. Appl., 9 (2016), 2857–2864]. Jang and Kim presented some identities of Fubini polynomials arising from differential equations in [G.-W. Jang, T. Kim, Adv. Studies Contem. Math., 28 (2018), to appear]. In this paper, we drive differential equations from the generating ...

Identities Involving Some New Special Polynomials Arising from the Applications of Fractional Calculus

Inspired by a number of recent investigations, we introduce the new analogues of the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials, the Apostol-Genocchi polynomials based on Mittag-Leffler function. Making use of the Caputo-fractional derivative, we derive some new interesting identities of these polynomials. It turns out that some known results are derived as special cases.

Multinomial identities arising from free probability theory

1.1. Overview. In order to answer some questions in the theory of operator algebras Dykema and Haagerup started investigation of the, so–called, triangular operator T [DH01]. Currently there are many different descriptions of this operator: in terms of random matrices, in terms of free probability theory and a purely combinatorial one (and we will recall them in the following). Dykema and Haage...

Non-degeneracy of Wiener Functionals Arising from Rough Differential Equations

Abstract. Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Itô map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss existence of a density for solutions to stochastic diff...

Fractional differential equations with Legendre polynomials