scholarly journals Iterative Positive Solutions to a Coupled Hadamard-Type Fractional Differential System on Infinite Domain with the Multistrip and Multipoint Mixed Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Xinran Du ◽  
Yuan Meng ◽  
Huihui Pang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Infinite Interval ◽  
Infinite Domain ◽  
Complete Continuity ◽  
Fractional Differential System ◽  
Fractional Differential

This paper is devoted to the existence of positive solutions for a nonlinear coupled Hadamard fractional differential system, with multistrip and multipoint mixed boundary conditions on an infinite interval. Based on the Arzelá-Ascoli theorem, we establish an important lemma to prove the complete continuity of operators on the infinite interval. Using the monotone iterative technique, the existence criteria for positive extremal solutions can be acquired, and an example is given to illustrate the feasibility of the above study as well.

scholarly journals Iterative positive solutions to a coupled fractional differential system with the multistrip and multipoint mixed boundary conditions

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiaodi Zhao ◽  
Yuehan Liu ◽  
Huihui Pang
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Mixed Boundary ◽  
Coupled System ◽  
Mixed Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Monotone Iterative ◽  
Fractional Differential System ◽  
Fractional Differential ◽  
Derivatives Of

Abstract Using the monotone iterative technique, we investigate the existence of iterative positive solutions to a coupled system of fractional differential equations supplemented with multistrip and multipoint mixed boundary conditions. It is worth mentioning that the nonlinear terms of the system depend on the lower fractional-order derivatives of the unknown functions and the boundary conditions involve the combination of the multistrip fractional integral and the multipoint value of the unknown functions in $[0,1]$ [ 0 , 1 ] .

scholarly journals Positive Solutions to a Coupled Fractional Differential System with p-Laplacian Operator

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Yuehan Liu ◽  
Xiaodi Zhao ◽  
Huihui Pang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Differential System ◽  
Fractional Derivatives ◽  
Existence Result ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Laplacian Operator ◽  
Fractional Differential System ◽  
Fractional Differential

In this paper, we consider a fractional differential system with multistrip and multipoint mixed boundary conditions involving p-Laplacian operator and fractional derivatives. The existence result of positive solutions is established by the Leggett-Williams fixed point theorem. Also, an example is presented to illustrate our main result.

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 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 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.

Sign in / Sign up

Export Citation Format

Share Document