Positive solutions to singular fractional differential system with coupled boundary conditions

2013 ◽  
Vol 18 (11) ◽  
pp. 3061-3074 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Differential System ◽  
Fractional Differential System ◽  
Coupled Boundary Conditions ◽  
Singular Fractional Differential System ◽  
Fractional Differential

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 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.

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