Paper Info
Title
Laplace type integral expressions for a certain three-parameter family of generalized Mittag-Leffler functions with applications involving complete monotonicity.
Abstract
In this paper, we derive a Laplace type integral expression for the function eα,βγ(t;λ) defined byeα,βγ(t;λ)≔tβ−1Eα,βγ(−λtα),where Eα,βγ(z) stands for the generalized three-parameter Mittag–Leffler function occurring in many interesting applied problems involving fractional differential equations. Our result is shown to enable us to extend certain findings by Mainardi (2010) [21] and others. As an application of the obtained Laplace type integral representation, we prove the complete monotonicity of the function eα,βγ(t;λ). We also establish several related positivity results and some uniform upper bounds for the function eα,βγ(t;λ).
Year
DOI
Venue
2014
10.1016/j.jfranklin.2014.09.007
Journal of the Franklin Institute
Field
DocType
Volume
Differential equation,Monotonic function,Mathematical optimization,Expression (mathematics),Laplace transform,Mathematical analysis,Integral representation,Mathematics
Journal
351
Issue
ISSN
Citations 
12
0016-0032
3
PageRank 
References 
Authors
0.51
4
3
Name
Order
Citations
PageRank
Zivorad Tomovski1254.18
Tibor Pogány23213.73
H.M. Srivastava330876.66