2017, ISBN 1786340887, xxii, 205 pages

Book

1992, 1, ISBN 0824784162, Volume 152., xi, 518

...). The five chapters are devoted to analytic continuation; conformal mappings, univalent functions, and nonconformal mappings; entire function; meromorphic fu

Functions of complex variables | Mathematical Analysis

Functions of complex variables | Mathematical Analysis

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2014, Volume 412, Issue 2, pp. 1058 - 1063

In this work, a Lyapunov-type inequality is obtained for the case when one is dealing with a fractional differential boundary value problem...

Caputoʼs fractional derivative | Lyapunovʼs inequality | Greenʼs function | Mittag–Leffler function | Lyapunov's inequality | Green's function | Caputo's fractional derivative | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | Equality

Caputoʼs fractional derivative | Lyapunovʼs inequality | Greenʼs function | Mittag–Leffler function | Lyapunov's inequality | Green's function | Caputo's fractional derivative | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | Equality

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 1, pp. 971 - 984

Some Turán type inequalities for Struve functions of the first kind are deduced by using various methods developed in the case of Bessel functions of the first and second kind...

Struve functions | Mittag–Leffler expansion | Turán type inequalities | Zeros of Struve functions | Bessel functions | Infinite product representation

Struve functions | Mittag–Leffler expansion | Turán type inequalities | Zeros of Struve functions | Bessel functions | Infinite product representation

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2017, Volume 20, Issue 5, pp. 1196 - 1215

Recently S. Gerhold and R. Garra – F. Polito independently introduced a new function related to the special functions of the Mittag-Leffler family...

Primary 33E12 | Mittag-Leffler and Wright functions | asymptotics | 30F15 | 35R11 | Secondary 30D10 | Laplace transforms | integral representation | special functions | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LEFFLER | EXPONENTIAL ASYMPTOTICS | EXPANSION | Functions | Laplace transformation | Research | Functional equations | Mathematical research

Primary 33E12 | Mittag-Leffler and Wright functions | asymptotics | 30F15 | 35R11 | Secondary 30D10 | Laplace transforms | integral representation | special functions | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | LEFFLER | EXPONENTIAL ASYMPTOTICS | EXPANSION | Functions | Laplace transformation | Research | Functional equations | Mathematical research

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2019, Volume 22, Issue 5, pp. 1284 - 1306

The paper [ ] by R. Garrappa, S. Rogosin, and F. Mainardi, entitled “On a generalized three-parameter Wright function of the Le Roy type” and published in . (2017), 1196...

Primary 33E12 | special functions of fractional calculus | Mittag-Leffler functions of Le Roy type (MLR functions) | completely monotonic functions | Secondary 26A33 | 26A48 | 32A17 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Integers | Parameters | Laplace transforms | Arrays | Mathematics - Classical Analysis and ODEs

Primary 33E12 | special functions of fractional calculus | Mittag-Leffler functions of Le Roy type (MLR functions) | completely monotonic functions | Secondary 26A33 | 26A48 | 32A17 | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Integers | Parameters | Laplace transforms | Arrays | Mathematics - Classical Analysis and ODEs

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2013, Volume 2, Issue 1, pp. 1 - 14

... a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated...

General Hurwitz-Lerch Zeta function | Lerch Zeta function and the Polylogarithmic (or de Jonquière’s) function | Hurwitz (or generalized) and Hurwitz-Lerch Zeta functions | Generating functions and Eulerian Gamma-function and Beta-function integral representations | Fox-Wright Ψ -function and the -function | Mittag-Leffler type functions | Gauss and Kummer hypergeometric functions | Mellin-Barnes type integral representations and Meromorphic continuation | Riemann | Science, general | Fox-Wright 9-function and the H-function | Lerch Zeta function and the Polylogarithmic (or de Jonquière's) function | Lerch Zeta function and the Polylogarithmic (or de Jonquiere's) function | SERIES | MULTIDISCIPLINARY SCIENCES | BERNOULLI | POLYNOMIALS | Fox-Wright Psi-function and the (H)over-bar-function | FEYNMAN-INTEGRALS | FORMULAS | EULER

General Hurwitz-Lerch Zeta function | Lerch Zeta function and the Polylogarithmic (or de Jonquière’s) function | Hurwitz (or generalized) and Hurwitz-Lerch Zeta functions | Generating functions and Eulerian Gamma-function and Beta-function integral representations | Fox-Wright Ψ -function and the -function | Mittag-Leffler type functions | Gauss and Kummer hypergeometric functions | Mellin-Barnes type integral representations and Meromorphic continuation | Riemann | Science, general | Fox-Wright 9-function and the H-function | Lerch Zeta function and the Polylogarithmic (or de Jonquière's) function | Lerch Zeta function and the Polylogarithmic (or de Jonquiere's) function | SERIES | MULTIDISCIPLINARY SCIENCES | BERNOULLI | POLYNOMIALS | Fox-Wright Psi-function and the (H)over-bar-function | FEYNMAN-INTEGRALS | FORMULAS | EULER

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2017, Volume 2017, Issue 1, pp. 1 - 6

In this paper, we show several Turán type inequalities for a generalized Mittag-Leffler function with four parameters via the ( p , k ) $(p,k)$ -gamma function.

33E12 | Analysis | Mathematics, general | Mathematics | Turán type inequalities | Applications of Mathematics | ( p , k ) $(p,k)$ -gamma function | 26D07 | generalized Mittag-Leffler function | (p, k) -gamma function | MATHEMATICS | Turan type inequalities | MATHEMATICS, APPLIED | (p,k)-gamma function | Gamma function | Inequalities | Research | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,k)$\end{document}(p,k)-gamma function

33E12 | Analysis | Mathematics, general | Mathematics | Turán type inequalities | Applications of Mathematics | ( p , k ) $(p,k)$ -gamma function | 26D07 | generalized Mittag-Leffler function | (p, k) -gamma function | MATHEMATICS | Turan type inequalities | MATHEMATICS, APPLIED | (p,k)-gamma function | Gamma function | Inequalities | Research | documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(p,k)$\end{document}(p,k)-gamma function

Journal Article

Applied mathematics and computation, ISSN 0096-3003, 2018, Volume 324, pp. 254 - 265

In this paper, we introduce a concept of delayed two parameters Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler matrix function...

Fractional delay differential equations | Finite time stability | Representation of solutions | Delayed two parameters Mittag-Leffler matrix function | Existence | LINEAR DISCRETE-SYSTEMS | MATHEMATICS, APPLIED | CONSTANT-COEFFICIENTS | PARTS | REPRESENTATION | APPROXIMATE CONTROLLABILITY | MILD SOLUTIONS | Differential equations

Fractional delay differential equations | Finite time stability | Representation of solutions | Delayed two parameters Mittag-Leffler matrix function | Existence | LINEAR DISCRETE-SYSTEMS | MATHEMATICS, APPLIED | CONSTANT-COEFFICIENTS | PARTS | REPRESENTATION | APPROXIMATE CONTROLLABILITY | MILD SOLUTIONS | Differential equations

Journal Article

Boletim da Sociedade Paranaense de Matematica, ISSN 0037-8712, 2020, Volume 38, Issue 5, pp. 165 - 174

This paper deals with a Euler type integral operator involving k-Mittag-Leffler function defined by Gupta and Parihar [8...

Generalized k-Wright function | Extended k-beta function | Euler type integrals | Generalized k-Mittag-Leffler function

Generalized k-Wright function | Extended k-beta function | Euler type integrals | Generalized k-Mittag-Leffler function

Journal Article

Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2017, Volume 102, pp. 184 - 196

This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives...

Feller process | Stopping time | β-stable subordinator | Boundary point | Generalised derivatives of Caputo type | Fractional evolution equation | Mittag–Leffler functions | DISTRIBUTED ORDER | ANOMALOUS DIFFUSION | Mittag-Leffler functions | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | beta-stable subordinator | PHYSICS, MATHEMATICAL | Differential equations | Mathematics - Analysis of PDEs

Feller process | Stopping time | β-stable subordinator | Boundary point | Generalised derivatives of Caputo type | Fractional evolution equation | Mittag–Leffler functions | DISTRIBUTED ORDER | ANOMALOUS DIFFUSION | Mittag-Leffler functions | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | beta-stable subordinator | PHYSICS, MATHEMATICAL | Differential equations | Mathematics - Analysis of PDEs

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 12/2013, Volume 16, Issue 4, pp. 978 - 984

In this work we obtain a Lyapunov-type inequality for a fractional differential equation subject to Dirichlet-type boundary conditions...

Abstract Harmonic Analysis | Functional Analysis | Analysis | Primary: 34A08, 34A40 | Mittag-Leffler function | fractional derivative, Green’s function | Secondary: 26D10, 34C10, 33E12 | Mathematics | Lyapunov’s inequality | Integral Transforms, Operational Calculus | fractional derivative, Green's function | Lyapunov's inequality | MATHEMATICS, APPLIED | fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Green's function

Abstract Harmonic Analysis | Functional Analysis | Analysis | Primary: 34A08, 34A40 | Mittag-Leffler function | fractional derivative, Green’s function | Secondary: 26D10, 34C10, 33E12 | Mathematics | Lyapunov’s inequality | Integral Transforms, Operational Calculus | fractional derivative, Green's function | Lyapunov's inequality | MATHEMATICS, APPLIED | fractional derivative | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Green's function

Journal Article

The Ramanujan journal, ISSN 1572-9303, 2018, Volume 50, Issue 2, pp. 263 - 287

..., such as Turán-type inequalities, Lazarević and Wilker-type inequalities. As applications we derive some new type inequalities for hypergeometric functions and the four-parametric Mittag–Leffler functions...

Hypergeometric functions | 33E12 | Functions of a Complex Variable | 33C20 | Field Theory and Polynomials | Lazarević and Wilker-type inequalities | Mathematics | Fox–Wright functions | Four-parametric Mittag–Leffler functions | Fourier Analysis | Turán-type inequalities | Number Theory | Combinatorics | 26D07 | Analysis | Television programs

Hypergeometric functions | 33E12 | Functions of a Complex Variable | 33C20 | Field Theory and Polynomials | Lazarević and Wilker-type inequalities | Mathematics | Fox–Wright functions | Four-parametric Mittag–Leffler functions | Fourier Analysis | Turán-type inequalities | Number Theory | Combinatorics | 26D07 | Analysis | Television programs

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 06/2019, Volume 69, Issue 3, pp. 573 - 582

We aim to present a new linear integral operator and a certain subclass of regular functions with bounded turning property in correlation with the extended generalised Mittag-Leffler functions...

Sălăgean integral operator | differential subordination | Mittag-Leffler functions | regular function | 30C50 | 30C85 | Secondary 30C55 | univalent function | Primary 30C45 | Salagean integral operator | MATHEMATICS | INEQUALITIES | CONVEX

Sălăgean integral operator | differential subordination | Mittag-Leffler functions | regular function | 30C50 | 30C85 | Secondary 30C55 | univalent function | Primary 30C45 | Salagean integral operator | MATHEMATICS | INEQUALITIES | CONVEX

Journal Article

The Annals of applied probability, ISSN 1050-5164, 8/2010, Volume 20, Issue 4, pp. 1303 - 1340

.... This rationale, and connection to the PD(α, Θ) distribution, motivates the investigations of its generalizations which we refer to as Lamperti-type...

Mathematical theorems | Coagulation | Positive laws | Markov processes | Eigenfunctions | Mathematical independent variables | Mathematical functions | Laplace transformation | Random variables | Poisson-Dirichlet distributions | Stable continuous state branching processes | Bessel bridges | Hyperbolic characteristic function | Mittag-Leffler function | Galton Watson limits | GAMMA | REPRESENTATIONS | stable continuous state branching processes | LINNIK | STATISTICS & PROBABILITY | TIME | MITTAG-LEFFLER FUNCTIONS | hyperbolic characteristic function | RANDOM-VARIABLES | BETA | DISTRIBUTIONS | PRODUCTS | ASYMPTOTICS | Mathematics - Probability | 60G09 | Mittag–Leffler function | 60E07 | Poisson–Dirichlet distributions

Mathematical theorems | Coagulation | Positive laws | Markov processes | Eigenfunctions | Mathematical independent variables | Mathematical functions | Laplace transformation | Random variables | Poisson-Dirichlet distributions | Stable continuous state branching processes | Bessel bridges | Hyperbolic characteristic function | Mittag-Leffler function | Galton Watson limits | GAMMA | REPRESENTATIONS | stable continuous state branching processes | LINNIK | STATISTICS & PROBABILITY | TIME | MITTAG-LEFFLER FUNCTIONS | hyperbolic characteristic function | RANDOM-VARIABLES | BETA | DISTRIBUTIONS | PRODUCTS | ASYMPTOTICS | Mathematics - Probability | 60G09 | Mittag–Leffler function | 60E07 | Poisson–Dirichlet distributions

Journal Article

Communications in nonlinear science & numerical simulation, ISSN 1007-5704, 2018, Volume 56, pp. 314 - 329

... are presented together with their applications to dielectric models of Havriliak–Negami type.•The asymptotic behavior of the Prabhakar function is studied in details...

Prabhakar function | Asymptotic expansion | Nonlinear heat equation | Prabhakar derivative | Mittag–Leffler function | Fractional calculus | Havriliak–Negami model | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | Havriliak-Negami model | ASYMPTOTIC-EXPANSION | REPRESENTATION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | Mittag-Leffler function | ANOMALOUS RELAXATION | OPERATORS | Derivatives (Financial instruments) | Electrical conductivity | Dielectrics

Prabhakar function | Asymptotic expansion | Nonlinear heat equation | Prabhakar derivative | Mittag–Leffler function | Fractional calculus | Havriliak–Negami model | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | Havriliak-Negami model | ASYMPTOTIC-EXPANSION | REPRESENTATION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | Mittag-Leffler function | ANOMALOUS RELAXATION | OPERATORS | Derivatives (Financial instruments) | Electrical conductivity | Dielectrics

Journal Article

Journal of Advanced Dielectrics, ISSN 2010-135X, 06/2019, Volume 9, Issue 3, pp. 1950021 - 1950021-4

...–Cole type response function or Havriliak–Negami type of dielectric relaxation. This work confirms completely the universality in chemical reaction kinetics, which can be described by fractional differential equations with Mittag...

Havriliak-Negami relaxation | Piezo-catalytic degradation | Mittag-Leffler function | Havriliak–Negami relaxation | Mittag–Leffler function

Havriliak-Negami relaxation | Piezo-catalytic degradation | Mittag-Leffler function | Havriliak–Negami relaxation | Mittag–Leffler function

Journal Article

18.
Full Text
Integral and computational representations of the extended Hurwitz–Lerch zeta function

Integral transforms and special functions, ISSN 1476-8291, 2011, Volume 22, Issue 7, pp. 487 - 506

.... We first establish their relationship with the -function, which enables us to derive the Mellin-Barnes type integral representations for nearly all of the generalized and specialized Hurwitz-Lerch Zeta functions...

analytic continuation | Fox-Wright Ψ-function | Mellin-Barnes type integral representations | gauss hypergeometric function | Primary: 11M25 | Riemann zeta function | Lerch zeta function | Mittag-Leffler type functions | general Hurwitz-Lerch zeta function | polylogarithmic function | H̄-function | Secondary: 33C05 | Mittag-leffler type functions | Gauss hypergeometric function | General hurwitz-lerch zeta function | Analytic continuation | Mellin-barnes type integral representations | Polylogarithmic function | Fox-wright ψ-function | TRANSFORMATION | MATHEMATICS, APPLIED | (H)over-bar-function | BERNOULLI | POLYNOMIALS | MATHEMATICS | FEYNMAN-INTEGRALS | EXPANSION | Fox-Wright Psi-function | FORMULAS | Studies

analytic continuation | Fox-Wright Ψ-function | Mellin-Barnes type integral representations | gauss hypergeometric function | Primary: 11M25 | Riemann zeta function | Lerch zeta function | Mittag-Leffler type functions | general Hurwitz-Lerch zeta function | polylogarithmic function | H̄-function | Secondary: 33C05 | Mittag-leffler type functions | Gauss hypergeometric function | General hurwitz-lerch zeta function | Analytic continuation | Mellin-barnes type integral representations | Polylogarithmic function | Fox-wright ψ-function | TRANSFORMATION | MATHEMATICS, APPLIED | (H)over-bar-function | BERNOULLI | POLYNOMIALS | MATHEMATICS | FEYNMAN-INTEGRALS | EXPANSION | Fox-Wright Psi-function | FORMULAS | Studies

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 2015, Volume 2015, Issue 1, pp. 1 - 10

In this paper, a Lyapunov-type inequality is obtained for a fractional differential equation under fractional boundary conditions...

Lyapunov inequality | Caputo fractional derivative | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | QUASI-LINEAR SYSTEMS | Liapunov functions | Analysis | Differential equations | Intervals | Boundary conditions | Difference equations | Inequalities

Lyapunov inequality | Caputo fractional derivative | Mittag-Leffler function | MATHEMATICS | MATHEMATICS, APPLIED | QUASI-LINEAR SYSTEMS | Liapunov functions | Analysis | Differential equations | Intervals | Boundary conditions | Difference equations | Inequalities

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2011, Volume 218, Issue 3, pp. 985 - 990

This paper is devoted to the study of a new special function, which is called, according to the symbol used to represent this function, as an Aleph function...

[formula omitted]-function | H-function | I-function | Mellin–Barnes type integrals | Riemann–Liouville fractional integral | Mittag–Leffler functions | Mittag-Leffler functions | Riemann-Liouville fractional integral | א-function | Mellin-Barnes type integrals | N-function | MATHEMATICS, APPLIED | FEYNMAN-INTEGRALS | Mathematical models | Biological | Computation | Mathematical analysis | Symbols

[formula omitted]-function | H-function | I-function | Mellin–Barnes type integrals | Riemann–Liouville fractional integral | Mittag–Leffler functions | Mittag-Leffler functions | Riemann-Liouville fractional integral | א-function | Mellin-Barnes type integrals | N-function | MATHEMATICS, APPLIED | FEYNMAN-INTEGRALS | Mathematical models | Biological | Computation | Mathematical analysis | Symbols

Journal Article