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

Authors

Serkan Araci, Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyFollow
Erdoğan Şen, Department of Mathematics, Faculty of Arts and Science, Namik Kemal University, TR-59030, Tekirdağ, Turkey\\ Department of Mathematics Engineering, Istanbul Technical University, Maslak, TR-34469 Istanbul, TurkeyFollow
Mehmet Acikgoz, Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, TR-27310 Gaziantep, TurkeyFollow
Kamil Oruçoğlu, Department of Mathematics Engineering, Istanbul Technical University, Maslak, TR-34469 Istanbul, TurkeyFollow

Author Country (or Countries)

Turkey

Abstract

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.

Recommended Citation

Araci, Serkan; Şen, Erdoğan; Acikgoz, Mehmet; and Oruçoğlu, Kamil (2015) "Identities Involving Some New Special Polynomials Arising from the Applications of Fractional Calculus," Applied Mathematics & Information Sciences: Vol. 09: Iss. 5, Article 51.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss5/51