Existence of positive solution for some class of nonlinear fractional differential equations
type: Item
instance of: scholarly article
title: Existence of positive solution for some class of nonlinear fractional differential equations
zbMATH Open document ID: 1026.34008
DOI: 10.1016/S0022-247X(02)00583-8
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-04T00:00:00Z
review text: The author considers nonlinear differential equations involving a generalised fractional differential operator corresponding to a generalised Riemann-Liouville fractional integral. He focuses on questions of existence and uniqueness of positive solutions to the equations. In the first two sections of the paper, the author introduces the definitions used, and gives basic theory. In Section 3, he gives a sequence of existence and uniqueness results followed by several lemmas and theorems that guarantee, under suitable conditions, the existence of multiple (infinite sequences of) positive solutions.
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1903477
zbMATH Keywords: fractional differential equations
zbMATH Keywords: positive solutions
author: Shuqin Zhang
reviewed by: Neville J. Ford
MaRDI profile type: Publication
cites work: Q3141902
cites work: Q3141895
cites work: Q4282622
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Some infinite series and functional relations that arose in the context of fractional calculus
cites work: Computation of fractional integrals via functions of hypergeometric and Bessel type
cites work: Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus
cites work: On Mittag-Leffler-type functions in fractional evolution processes
cites work: Explicit solutions of fractional integral and differential equations involving Erdélyi-Kober operators
cites work: Explicit solutions to hyper-Bessel integral equations of second kind
cites work: Fractional-order diffusion-wave equation
cites work: On the fractional differential equations
cites work: Nonlinear functional differential equations of arbitrary orders
cites work: Existence and uniqueness for a nonlinear fractional differential equation
cites work: The existence of a positive solution for a nonlinear fractional differential equation
cites work: A class of analytic functions defined by fractional derivation
cites work: Q5732050
full work available at URL: s0022-247x(02)00583-8
OpenAlex ID: W2061961789
description: scientific article; zbMATH DE number 1903477