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

An extended generalized q -extensions for the apostol type polynomials

Through a modification on the parameters associated with generating function of the q-extensions for the Apostol type polynomials of order and level m, we obtain some new results related to a unified presentation of the q-analog of the generalized Apostol type polynomials of order and level m. In addition, we introduce some algebraic and differential properties for the q-analog of the generalized Apostol type polynomials of order and level m and the relation of these with the q-Stirling numbers of the second kind, the generalized q-Bernoulli polynomials of level m, the generalized q-Apostol type Bernoulli polynomials, the generalized q-Apostol type Euler polynomials, the generalized q-Apostol type Genocchi polynomials of order and level m, and the q-Bernstein polynomials. © 2018 Letelier Castilla et al

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the convolutions of Bernoulli and Euler polynomials, expressed via Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte