A further extension of Mittag-Leffler function

In this paper an extended generalized Mittag-Leffler function and the corresponding fractional integral operator are defined and used to obtain generalizations of Opial-type inequalities due to Mitrinović and Pečarić. Also, some interesting properties of this function and its integral operator are d...

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Bibliographic Details
Published inFractional calculus & applied analysis Vol. 21; no. 5; pp. 1377 - 1395
Main Authors Andrić, Maja, Farid, Ghulam, Pečarić, Josip
Format Journal Article
LanguageEnglish
Published Warsaw Versita 25.10.2018
De Gruyter
Walter de Gruyter GmbH
Subjects
26D15
33E12
Abstract Harmonic Analysis
Analysis
Arrays
fractional calculus
Functional Analysis
Integral Transforms
Integrals
Mathematics
Mittag-Leffler function
Operational Calculus
Operators (mathematics)
Opial’s inequality
Primary 26A33
Research Paper
Secondary 26D10
33E12
fractional calculus
Primary 26A33
Secondary 26D10
Mittag-Leffler function
26D15
Opial’s inequality
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Summary:In this paper an extended generalized Mittag-Leffler function and the corresponding fractional integral operator are defined and used to obtain generalizations of Opial-type inequalities due to Mitrinović and Pečarić. Also, some interesting properties of this function and its integral operator are discussed. Several known results are deduced.
ISSN:1311-0454
1314-2224
DOI:10.1515/fca-2018-0072