scholarly journals Monotone iterative schemes for positive solutions of a fractional differential system with integral boundary conditions on an infinite interval

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4399-4417
Author(s):  
Yaohong Li ◽  
Wei Cheng ◽  
Jiafa Xu
Keyword(s):  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Contraction Mapping Principle ◽  
Infinite Interval ◽  
Integral Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, using the monotone iterative technique and the Banach contraction mapping principle, we study a class of fractional differential system with integral boundary on an infinite interval. Some explicit monotone iterative schemes for approximating the extreme positive solutions and the unique positive solution are constructed.

scholarly journals Positive Solutions for(n-1,1)-Type Singular Fractional Differential System with Coupled Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Ying Wang ◽  
Lishan Liu ◽  
Xinguang Zhang ◽  
Yonghong Wu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Coupled Integral Boundary Conditions ◽  
Existence Of Positive Solutions ◽  
Singular Fractional Differential System ◽  
Fractional Differential

We study the positive solutions of the(n-1,1)-type fractional differential system with coupled integral boundary conditions. The conditions for the existence of positive solutions to the system are established. In addition, we derive explicit formulae for the estimation of the positive solutions and obtain the unique positive solution when certain additional conditions hold. An example is then given to demonstrate the validity of our main results.

scholarly journals Positive solutions to n-dimensional $\alpha _{1}+\alpha _{2}$ order fractional differential system with p-Laplace operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Tian Wang ◽  
Guo Chen ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Laplace Operator ◽  
Positive Solutions ◽  
Differential System ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Fractional Differential

AbstractIn this paper, we study an n-dimensional fractional differential system with p-Laplace operator, which involves multi-strip integral boundary conditions. By using the Leggett–Williams fixed point theorem, the existence results of at least three positive solutions are established. Besides, we also get the nonexistence results of positive solutions. Finally, two examples are presented to validate the main results.

scholarly journals Results of Positive Solutions for the Fractional Differential System on an Infinite Interval

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ying Wang ◽  
Jun Yang ◽  
Yumei Zi
Keyword(s):  
Positive Solutions ◽  
Differential System ◽  
Contraction Mapping Principle ◽  
Infinite Interval ◽  
Compactness Criterion ◽  
Fractional Differential System ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Banach Contraction Mapping Principle ◽  
Banach Contraction Mapping

The chief topic of this paper is to investigate the fractional differential system on an infinite interval. By introducing an appropriate compactness criterion in a special function space and applying the Schauder fixed-point theorem and the Banach contraction mapping principle, we established the results for the existence and uniqueness of positive solutions. An example is then given to show the utilization of the main results.

scholarly journals Positive solutions for singular semipositone nonlinear fractional differential system

Filomat ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 169-179
Author(s):  
Rim Bourguiba ◽  
Faten Toumi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential System ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, under suitable conditions we employ the nonlinear alternative of Leray-Schauder type and the Guo-Krasnosel?skii fixed point theorem to show the existence of positive solutions for a system of nonlinear singular Riemann-Liouville fractional differential equations with sign-changing nonlinearities, subject to integral boundary conditions. Some examples are given to illustrate our main results.

scholarly journals Positive Solutions for Singularp-Laplacian Fractional Differential System with Integral Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Liping Wang ◽  
Zongfu Zhou ◽  
Hui Zhou
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Value System ◽  
Fractional Differential System ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fractional differential equations with integral boundary conditions. By using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions to the boundary value system is guaranteed.

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