A new generalization of Mittag-Leffler function via q-calculus

The present paper deals with a new different generalization of the Mittag-Leffler function through q -calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q -derivative formula, q -Laplace transformation, and image formula under q -d...

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Bibliographic Details
Published in:Advances in difference equations Vol. 2020; no. 1; pp. 1 - 10
Main Authors: Nadeem, Raghib, Usman, Talha, Nisar, Kottakkaran Sooppy, Abdeljawad, Thabet
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 09.12.2020
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications
Calculus
Derivatives
Difference and Functional Equations
Functional Analysis
Integrals
Mathematics
Mathematics and Statistics
Methods
Mittag-Leffler function
Operators (mathematics)
Ordinary Differential Equations
Partial Differential Equations
q-beta functions
q-gamma functions
Topics in Special Functions and q-Special Functions: Theory
33C47
gamma functions
33C45
Mittag-Leffler function
beta functions
33C90
33C05
ISSN:1687-1847, 1687-1839, 1687-1847
Online Access:Get full text
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Summary:The present paper deals with a new different generalization of the Mittag-Leffler function through q -calculus. We then investigate its remarkable properties like convergence, recurrence relation, integral representation, q -derivative formula, q -Laplace transformation, and image formula under q -derivative operator. In addition to this, we consider some specific cases to give the utilization of our main results.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-020-03157-z