Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters

By Limin Guo, Lishan Liu, Yonghong Wu. 2018

52 citations recorded by the source corpus.

By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann–Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/ef19d34e257bbe42ffe6047922fd6e49de1cf799

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yujun Cui
2. Xinguang Zhang
3. Lishan Liu
4. Yonghong Wu
5. Aziz Khan
6. Hasib Khan
7. Cemil Tunç

In Modeling and Simulation

1. Yujun Cui
2. Xinguang Zhang
3. Lishan Liu
4. Yonghong Wu
5. Aziz Khan
6. Hasib Khan
7. Cemil Tunç

Citations in the corpus

• A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator (2020, methodology): “Here, in order to make the article more complete, we also recall some analysis methods and numerical techniques, which have been used to study various nonlinear ordinary differential equations and partial differential equations such as iterative methods [9, 11, 28, 29, 42, 43, 48, 54, 60, 61, 72, 76”
• STABILITY RESULTS AND EXISTENCE THEOREMS FOR NONLINEAR DELAY-FRACTIONAL DIFFERENTIAL EQUATIONS WITH $ \varphi^*_P $-OPERATOR (2020, background): “[11] proved uniqueness theorems for position solutions of a singular fractional DE with nonlinear φp-operator and Riemann-Stieltjes type boundary conditions.”