On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$
暂无分享,去创建一个
[1] Harry Pollard,et al. The completely monotonic character of the Mittag-Leffler function $E_a \left( { - x} \right)$ , 1948 .
[2] V. Kiryakova,et al. The Multi-index Mittag-Leffler Functions and Their Applications for Solving Fractional Order Problems in Applied Analysis , 2010 .
[3] K. Diethelm. Mittag-Leffler Functions , 2010 .
[4] Hari M. Srivastava,et al. The H-functions of one and two variables, with applications , 1982 .
[5] A. M. Mathai,et al. The H-Function: Theory and Applications , 2009 .
[6] K. Diethelm,et al. Fractional Calculus: Models and Numerical Methods , 2012 .
[7] R. Gorenflo,et al. Time-fractional derivatives in relaxation processes: a tutorial survey , 2008, 0801.4914.
[8] Arak M. Mathai,et al. The H-function with applications in statistics and other disciplines , 1978 .
[9] Ralf Metzler,et al. Fractional dynamics : recent advances , 2011 .
[10] K. Cole,et al. Dispersion and Absorption in Dielectrics II. Direct Current Characteristics , 1942 .
[11] Ralf Metzler,et al. Velocity and displacement correlation functions for fractional generalized Langevin equations , 2012 .
[12] G. A. Baker. Essentials of Padé approximants , 1975 .
[13] H. M. Srivastava,et al. Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions , 2010 .
[14] R. Magin. Fractional Calculus in Bioengineering , 2006 .
[15] K. Miller,et al. Completely monotonic functions , 2001 .
[16] E. Hille,et al. On the Theory of Linear Integral Equations. II , 1930 .
[17] Sergei V. Rogosin,et al. Multi-parametric mittag-leffler functions and their extension , 2013 .
[18] Anatoly A. Kilbas,et al. On solution of integral equation of Abel-Volterra type , 1995, Differential and Integral Equations.
[19] William Feller,et al. An Introduction to Probability Theory and Its Applications , 1967 .
[20] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[21] B. Gross,et al. On Creep and Relaxation , 1947 .
[22] Arak M. Mathai,et al. Special Functions for Applied Scientists , 2008 .
[23] M. Caputo,et al. A new dissipation model based on memory mechanism , 1971 .
[24] F. Mainardi,et al. Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics , 2011, 1106.1761.
[25] A. P. Starovoitov,et al. Padé approximants of the Mittag-Leffler functions , 2007 .
[26] Giovanni Sansone,et al. Lectures on the theory of functions of a complex variable , 1961 .
[27] R. Gorenflo,et al. Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.
[28] N. Ford,et al. Analysis of Fractional Differential Equations , 2002 .
[29] K. Cole,et al. Dispersion and Absorption in Dielectrics I. Alternating Current Characteristics , 1941 .
[30] Francesco Mainardi,et al. Linear models of dissipation in anelastic solids , 1971 .
[31] M. T. Cicero. FRACTIONAL CALCULUS AND WAVES IN LINEAR VISCOELASTICITY , 2012 .
[32] Arak M. Mathai,et al. The H-Function , 2010 .
[33] A. Erdélyi,et al. Higher Transcendental Functions , 1954 .
[34] Hiroshi Yamauchi,et al. Lectures on the Theory of Functions of a Complex Variable, Vol. I, Holomorphic Functions. , 1961 .
[35] René L. Schilling,et al. Bernstein Functions: Theory and Applications , 2010 .
[36] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[37] V. E. Tarasov. Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media , 2011 .
[38] Thomas Simon,et al. Comparing Fréchet and positive stable laws , 2013, 1310.1888.
[39] O. I. Marichev,et al. Handbook of Integral Transforms of Higher Transcendental Functions , 1983 .
[40] A. Kilbas. H-Transforms: Theory and Applications , 2004 .
[41] I. Podlubny. Fractional differential equations , 1998 .
[42] V. Kiryakova,et al. The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus , 2010, Comput. Math. Appl..
[43] Luisa Beghin,et al. Poisson-type processes governed by fractional and higher-order recursive differential equations , 2009, 0910.5855.
[44] V. Kiryakova. Generalized Fractional Calculus and Applications , 1993 .
[45] Wong,et al. Exponential Asymptotics of the Mittag—Leffler Function , 2002 .
[46] V. Uchaikin. Fractional Derivatives for Physicists and Engineers , 2013 .