Identities involving some new special polynomials arising from the applications of fractional calculus

Serkan Araci; Erdoğan Şen; Mehmet Acikgoz; Kamil Oruçoğlu

doi:10.12785/amis/090551

Identities involving some new special polynomials arising from the applications of fractional calculus

Serkan Araci^*, Erdoğan Şen, Mehmet Acikgoz, Kamil Oruçoğlu

^*Corresponding author for this work

Department of Mathematics Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	2657-2662
Number of pages	6
Journal	Applied Mathematics and Information Sciences
Volume	9
Issue number	5
DOIs	https://doi.org/10.12785/amis/090551
Publication status	Published - 2015

Bibliographical note

Publisher Copyright:
© 2015 NSP Natural Sciences Publishing Cor.

Keywords

Apostol-bernoulli polynomials
Apostol-euler polynomials
Apostol-genocchi polynomials
Caputo-fractional derivative
Mittag-leffler function

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10.12785/amis/090551

Cite this

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title = "Identities involving some new special polynomials arising from the applications of fractional calculus",

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.",

keywords = "Apostol-bernoulli polynomials, Apostol-euler polynomials, Apostol-genocchi polynomials, Caputo-fractional derivative, Mittag-leffler function",

author = "Serkan Araci and Erdoğan {\c S}en and Mehmet Acikgoz and Kamil Oru{\c c}oğlu",

note = "Publisher Copyright: {\textcopyright} 2015 NSP Natural Sciences Publishing Cor.",

year = "2015",

doi = "10.12785/amis/090551",

language = "English",

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pages = "2657--2662",

journal = "Applied Mathematics and Information Sciences",

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T1 - Identities involving some new special polynomials arising from the applications of fractional calculus

AU - Araci, Serkan

AU - Şen, Erdoğan

AU - Acikgoz, Mehmet

AU - Oruçoğlu, Kamil

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Apostol-bernoulli polynomials

KW - Apostol-euler polynomials

KW - Apostol-genocchi polynomials

KW - Caputo-fractional derivative

KW - Mittag-leffler function

UR - https://www.scopus.com/pages/publications/84937848981

U2 - 10.12785/amis/090551

DO - 10.12785/amis/090551

M3 - Article

AN - SCOPUS:84937848981

SN - 1935-0090

VL - 9

SP - 2657

EP - 2662

JO - Applied Mathematics and Information Sciences

JF - Applied Mathematics and Information Sciences

IS - 5

ER -

Identities involving some new special polynomials arising from the applications of fractional calculus

Abstract

Bibliographical note

Keywords

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