Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation with deviating arguments

Hu, Chaozhu; Liu, Bin; Xie, Shouyi

doi:10.1016/j.amc.2013.07.048

Cited by 24 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is clear that the solution of [20] is concave when ( ) ≥ 0 on [0, 1] and ( ) ≥ 0 on [0, ∞). However, few papers have reported the same problems where the solution is without concavity; for example, see some recent excellent results and applications of the case of ordinary differential equations with deviating arguments to a variety of problems from Jankowski [21][22][23], Jiang and Wei [24], Wang [25], Wang et al [26], and Hu et al [27]. This paper will resolve this problem.…”

Section: Introductionmentioning

confidence: 84%

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Zhang

Feng

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

This paper investigates the expression and properties of Green’s function for a second-order singular boundary value problem with integral boundary conditions and delayed argument-x′′t-atx′t+btxt=ωtft, xαt, t∈0, 1; x′0=0, x1-∫01htxtdt=0, wherea∈0, 1, 0, +∞, b∈C0, 1, 0, +∞and,ωmay be singular att=0or/and att=1. Furthermore, several new and more general results are obtained for the existence of positive solutions for the above problem by using Krasnosel’skii’s fixed point theorem. We discuss our problems with a delayed argument, which may concern optimization issues of some technical problems. Moreover, the approach to express the integral equation of the above problem is different from earlier approaches. Our results cover a second-order boundary value problem without deviating arguments and are compared with some recent results.

show abstract

Section: Introductionmentioning

confidence: 84%

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Zhang

Feng

2014

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

“…For examples and details, see [23][24][25][26][27][28][29][30][31][32]. Motivated by this approach, we seek the extremal solutions for the problem (1.1).…”

Section: Introductionmentioning

confidence: 99%

Explicit iterations and extremal solutions for fractional differential equations with nonlinear integral boundary conditions

Zhang

Ahmad

Wang

2015

Applied Mathematics and Computation

View full text Add to dashboard Cite

“…By means of the monotone iterative method, they proved the existence of a positive solution and established an iterative sequence for approximating the solution to BVP (2). For relevant results, one can refer to [22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

Sun

Zhao

2020

Discrete Dynamics in Nature and Society

View full text Add to dashboard Cite

In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper.

show abstract

Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation with deviating arguments

Cited by 24 publications

References 8 publications

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Green’s Function and Positive Solutions for a Second-Order Singular Boundary Value Problem with Integral Boundary Conditions and a Delayed Argument

Explicit iterations and extremal solutions for fractional differential equations with nonlinear integral boundary conditions

Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

Contact Info

Product

Resources

About