Solvability of some two-point fractional boundary value problems under barrier strip conditions
type: Item
instance of: scholarly article
title: Solvability of some two-point fractional boundary value problems under barrier strip conditions
zbMATH Open document ID: 1381.34015
DOI: 10.1155/2017/1465623
author: Limei He
author: Xiaoyu Dong
author: Zhanbing Bai
author: Bo Chen
published in: Journal of Function Spaces
publication date: 2017-12-06T00:00:00Z
review text: Summary: Topological techniques are used to establish existence results for a class of fractional differential equations \[ D^\alpha x(t) = f(t, x(t), D^{\alpha - 1} x(t)) \] with one of the following boundary value conditions: \[ x(0) = A \text{ and } D^{\alpha - 1} x(1) = B \text{ or } D^{\alpha - 1} x(0) = A \text{ and } x(1) = B, \] where \(1 < \alpha \leq 2\) is a real number, \(D^\alpha x(t)\) is the conformable fractional derivative, and \(f : [0,1] \times \mathbb R^2 \rightarrow \mathbb R\) is continuous. The main conditions on the nonlinear term \(f\) are sign conditions (i.e., the barrier strip conditions). The topological arguments are based on the topological transversality theorem.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6816051
zbMATH Keywords: sign conditions
zbMATH Keywords: topological transversality theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1465623
OpenAlex ID: W2765871170
cites work: The existence of a positive solution for a nonlinear fractional differential equation
cites work: On positive solutions of a nonlocal fractional boundary value problem
cites work: Existence results for impulsive nonlinear fractional differential equation with mixed boundary conditions
cites work: Q3466975
cites work: Solvability of fractional three-point boundary value problems with nonlinear growth
cites work: The existence of solutions for a fractional multi-point boundary value problem
cites work: Existence of positive solution for singular fractional differential equation
cites work: Uniqueness of solution for boundary value problems for fractional differential equations
cites work: Generalized fractional supertrace identity for Hamiltonian structure of NLS-MKdV hierarchy with self-consistent sources
cites work: Positive solutions to boundary value problems of \(p\)-Laplacian with fractional derivative
cites work: On the ground state solution for a critical fractional Laplacian equation
cites work: A New Approach to Generalized Fractional Derivatives
cites work: On the iterative learning control for stochastic impulsive differential equations with randomly varying trial lengths
cites work: The method of lower and upper solutions for mixed fractional four-point boundary value problem with \(p\)-Laplacian operator
cites work: Existence and uniqueness of solution for fractional differential equations with integral boundary conditions
cites work: Dynamics of a novel nonlinear stochastic SIS epidemic model with double epidemic hypothesis
cites work: Traveling waves in a generalized nonlinear dispersive–dissipative equation
cites work: Existence for fractional Dirichlet boundary value problem under barrier strip conditions
cites work: Comments on the concept of existence of solution for impulsive fractional differential equations
cites work: On recent developments in the theory of boundary value problems for impulsive fractional differential equations
cites work: A numerical method for delayed fractional-order differential equations
cites work: Geometric singular perturbation method to the existence and asymptotic behavior of traveling waves for a generalized Burgers-KdV equation
cites work: Equations involving fractional Laplacian operator: compactness and application
cites work: Solutions of fractional Laplacian equations and their Morse indices
cites work: Extremal solutions for some periodic fractional differential equations
cites work: Existence results for a functional boundary value problem of fractional differential equations
cites work: Existence of solutions for two-point boundary value problems
cites work: Singular and nonsingular first-order initial value problems
cites work: Applications of topological transversality to differential equations. I: Some nonlinear diffusion problems
Recommended article: Existence of solutions for some two-point fractional boundary value problems under barrier strip conditions
Recommended article: Solvability of a two-point fractional boundary value problem
Recommended article: Existence for fractional Dirichlet boundary value problem under barrier strip conditions
Recommended article: Solvability of a class of higher-order fractional two-point boundary value problem
Recommended article: Two point fractional boundary value problems with a fractional boundary condition
Recommended article: Two-point fractional boundary value problems
Recommended article: Q5257440
Recommended article: Existence of solution for some two-point boundary value fractional differentialequations
Recommended article: Q3188550
Recommended article: Q3131070
description: scientific article; zbMATH DE number 6816051