scholarly journals A uniqueness method to a new Hadamard fractional differential system with four-point boundary conditions

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Chengbo Zhai ◽  
Weixuan Wang ◽  
Hongyu Li
Keyword(s):  
Boundary Conditions ◽  
Differential System ◽  
Point Boundary ◽  
Fractional Differential System ◽  
Uniqueness Method ◽  
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 Uniqueness of iterative positive solutions for the singular infinite-point p-Laplacian fractional differential system via sequential technique

2020 ◽  
Vol 25 (5) ◽  
Author(s):  
Limin Guo ◽  
Lishan Liu ◽  
Yanqing Feng
Keyword(s):  
Positive Solutions ◽  
Differential System ◽  
Iterative Sequence ◽  
Point Boundary ◽  
Practical Application ◽  
Mixed Monotone Operator ◽  
Fractional Differential System ◽  
Infinite Point ◽  
Fractional Differential ◽  
Sequential Technique

By sequential techniques and mixed monotone operator, the uniqueness of positive solution for singular p-Laplacian fractional differential system with infinite-point boundary conditions is obtained. Green's function is derived, and some useful properties of Green' function are obtained. Based on these new properties, the existence of unique positive solutions is established, moreover, an iterative sequence and a convergence rate are given, which are important for practical application, and an example is given to demonstrate the validity of our main results.

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