Naslov
Laplace type integral expressions for a certain three-parameter family of generalized Mittag– Leffler functions with applications involving complete monotonicity

Autori
Tomovski, Živorad ; Poganj, Tibor ; Srivastava, Hari M.

Izvornik
Journal of the Franklin institute-engineering and applied mathematics (0016-0032) 351 (2014), 12; 5437-5454

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Three parameter Mittag-Leffler function; Laplace integral representation; Complete monotonicity; Bounding inequality

Sažetak
In this paper, we derive a Laplace type integral expression for the function $e(t) = t^{; ; \beta-1}; ; ; E_{; ; \alpha, \beta}; ; ^\gamma(-\lambda t^\alpha)$ where $E$ 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 $e(t)$. We also establish several related positivity results and some uniform upper bounds for the function $e(t)$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA