Fractional differential equations for the generalized Mittag-Leffler function View Full Text


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Article Info

DATE

2018-02-15

AUTHORS

Praveen Agarwal, Qasem Al-Mdallal, Yeol Je Cho, Shilpi Jain

ABSTRACT

In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{3}(\cdot)$\end{document} and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}_{m+1}\psi^{(\{\kappa_{l}\}_{l\in\mathbb{N}_{0}} )}_{n+1}(z; p)$\end{document} recently established by Agarwal. Some interesting special cases are also pointed out. More... »

PAGES

58

References to SciGraph publications

  • 2012-12-19. Some identities involving Gegenbauer polynomials in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2013-03-19. Fractional Integration of the Product of Two Multivariables H-Function and a General Class of Polynomials in ADVANCES IN APPLIED MATHEMATICS AND APPROXIMATION THEORY
  • 2014-02-20. The extended Mittag-Leffler function and its properties in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2017. Advances in Real and Complex Analysis with Applications in NONE
  • 2017-10. Further extended Caputo fractional derivative operator and its applications in RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS
  • 2015-12-05. A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems in FRACTIONAL CALCULUS AND APPLIED ANALYSIS
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    http://scigraph.springernature.com/pub.10.1186/s13662-018-1500-7

    DOI

    http://dx.doi.org/10.1186/s13662-018-1500-7

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