Identities Involving Some New Special Polynomials Arising from the Applications of Fractional Calculus - Aracı, Serkan; Şen, Erdoğan; Açıkgöz, Mehmet; Oruçoğlu, Kamil; Aracı, Serkan (My University, 2016)
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.
Keywords: Mittag-Leffler function, Caputo-Fractional derivative, Apostol-Bernoulli polynomials, Apostol-Genocchi polynomials, Apostol-Euler polynomials