On pseudo-Mittag-Leffler functions and applications

被引：8

作者：

Agahi, Hamzeh ^{[1
]}

Alipour, Mohsen ^{[1
]}

机构：

[1] Babol Noshirvani Univ Technol, Fac Basic Sci, Dept Math, POB 47148-71167, Babol Sar, Iran

来源：

FUZZY SETS AND SYSTEMS | 2017年 / 327卷

关键词：

Distribution of zeros; Pseudo-Mittag-Leffler functions; Pseudo-fractional derivative; LYAPUNOV-TYPE INEQUALITY;

D O I：

10.1016/j.fss.2016.11.011

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

The Mittag-Leffer function and related distribution are valuable in statistics, applied mathematics and lifetime data analysis. In this paper, we introduce the concept of pseudo-Mittag-Leffler functions. Then, we discuss the pseudo-fractional boundary value problems in two classes of pseudo-Caputo fractional derivative and pseudo-Riemann-Liouville fractional derivative to get the pseudo-integral inequalities of Lyapunov-type. Also, as an application, we obtain the nonexistence of real zeros of pseudo-Mittag-Leffler functions. Our results generalize the corresponding ones in the literature. Finally, two open problems for further investigations are given. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：21 / 30

页数：10

共 28 条

[1] Chebyshev type inequalities for pseudo-integrals [J].

Agahi, Hamzeh ;

Mesiar, Radko ;

Ouyang, Yao .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2737-2743

[2] On the concept of solution for fractional differential equations with uncertainty [J].

Agarwal, Ravi P. ;

Lakshmikantham, V. ;

Nieto, Juan J. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) :2859-2862

[3] Solving multi-dimensional fractional optimal control problems with inequality constraint by Bernstein polynomials operational matrices [J].

Alipour, Mohsen ;

Rostamy, Davood ;

Baleanu, Dumitru .

JOURNAL OF VIBRATION AND CONTROL, 2013, 19 (16) :2523-2540

[4]

[Anonymous], 2006, Journal of the Electrochemical Society

[5] The theory of pseudo-linear operators [J].

Bede, Barnabas ;

O'Regan, Donal .

KNOWLEDGE-BASED SYSTEMS, 2013, 38 :19-26

[6] On a Lyapunov-type inequality and the zeros of a certain Mittag-Leffler function [J].

Ferreira, Rui A. C. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 412 (02) :1058-1063

[7] A Lyapunov-type inequality for a fractional boundary value problem [J].

Ferreira, Rui A. C. .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (04) :978-984

[8]

Kuich W., 1986, Semirings, Automata, Languages, DOI [10.1007/978-3-642-69959-7, DOI 10.1007/978-3-642-69959-7]

[9] Fractional Poisson process [J].

Laskin, Nick .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2003, 8 (3-4) :201-213

[10]

Lyapunov A.M. A. M., 1907, Ann. Fac. Sci. Univ. Toulouse, V2, P27

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