On a new class of functions related with Mittag-Leffler and Wright functions and their properties
0
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In the present paper, we define new class of functions \linebreak $T_{\alpha, \beta}(\lambda;z)$ which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Tur\'{a}n-type inequalities, Lazarevi\'{c}-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function $T_{\alpha, \beta}(\lambda;z)$ are presented.
Abstract
In the present paper, we define new class of functions \linebreak $T_{\alpha, \beta}(\lambda;z)$ which is an extension of the classical Wright function and the Mittag-Leffler function. We show some mean value inequalities for the this function, such as Tur\'{a}n-type inequalities, Lazarevi\'{c}-type inequalities and Wilker-type inequalities. Moreover, integrals formula and integral inequality for the function $T_{\alpha, \beta}(\lambda;z)$ are presented.
참고문헌 (13)
- M. M. Dˇzrbaˇsjan, "Integral transforms and representations of functions in the complex domain (Russian), Izdat" (1966), Nauka
- A. Erd´elyi, "Higher Transcendental Functions, Vol. 3" (1955), McGraw-Hill
- R. Gorenflo, "Analytic properties and applications of Wright functions", Frac. Cal. Appl. Anal, 2(4), pp.383~414 (1999)
- R. Hilfer, "Applications of Fractional Calculus in Physics" (2000), World Scientific Publishing Co., Inc.
- K. R. Lang, "Astrophysical Formulae, Vol. 1: Radiation, Gas Processes and High-energy Astrophysics" (1999), Springer-Verlag
- K. R. Lang, "Astrophysical Formulae, Vol. 2: Space, Time, Matter and Cosmology" (1999), SpringerVerlag
- F. Mainardi, "The fundamental solutions for the fractional diffusion-wave equation", Appl. Math. Lett, 9(6), pp.23~28 (1996)[DOI]
- K. Mehrez, "Functional inequalities for the Wright functions", Integral Transforms Spec. Funct, 28(2), pp.130~144 (2017)[DOI]
- K. Mehrez, "Functional inequalities for the Mittag-Leffler functions", Results Math, 72(1-2), pp.703~714 (2017)[DOI]
- K. Mehrez, "Tur´an type inequalities for classical and generalized Mittag-Leffler functions", Anal. Math, 44(4), pp.521~541 (2018)[DOI]
- S. Ponnusamy, "Asymptotic expansions and inequalities for hypergeometric functions", Mathematika, 44(2), pp.278~301 (1997)[DOI]
- R. K. Saxena, "On fractional kinetic equations", Astrophysics and Space Science, 282, pp.281~287 (2002)
- E. M. Wright, "On the Coefficients of Power Series Having Exponential Singularities", J. London Math. Soc, 8(1), pp.71~79 (1933)[DOI]