scholarly journals Eigenvalue of Fractional Differential Equations withp-Laplacian Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wenquan Wu ◽  
Xiangbing Zhou
Keyword(s):  
Differential Equation ◽  
Eigenvalue Problem ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Upper And Lower Solutions ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We investigate the existence of positive solutions for the fractional order eigenvalue problem withp-Laplacian operator-𝒟tβ(φp(𝒟tαx))(t)=λf(t,x(t)),  t∈(0,1),  x(0)=0,  𝒟tαx(0)=0,  𝒟tγx(1)=∑j=1m-2‍aj𝒟tγx(ξj), where𝒟tβ,  𝒟tα,  𝒟tγare the standard Riemann-Liouville derivatives andp-Laplacian operator is defined asφp(s)=|s|p-2s,  p>1.f:(0,1)×(0,+∞)→[0,+∞)is continuous andfcan be singular att=0,1andx=0.By constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of fractional differential equation is established.

scholarly journals Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3031
Author(s):  
Weiwei Liu ◽  
Lishan Liu
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Lower Order ◽  
Higher Order ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Weaker Conditions

This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

scholarly journals Positive Solutions of Eigenvalue Problems for a Class of Fractional Differential Equations with Derivatives

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Benchawan Wiwatanapataphee ◽  
Yonghong Wu
Keyword(s):  
Eigenvalue Problem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Maximal Principle

By establishing a maximal principle and constructing upper and lower solutions, the existence of positive solutions for the eigenvalue problem of a class of fractional differential equations is discussed. Some sufficient conditions for the existence of positive solutions are established.

scholarly journals Positive solutions of boundary value problems for p-Laplacian fractional differential equations

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1265-1277 ◽  
Author(s):  
Fatma Fen ◽  
Ilkay Karac ◽  
Ozlem Ozen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

This work is devoted to the existence of positive solutions for nonlinear fractional differential equations with p-Laplacian operator. By using five functionals fixed point theorem, the existence of at least three positive solutions are obtained. As an application, an example is presented to demonstrate our main result.

scholarly journals Positive Solutions for a System of Fractional Differential Equations with Two Parameters

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Hongyu Li ◽  
Junting Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Differential Equations ◽  
Laplacian Operator ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Two Parameters

In this paper, the existence of positive solutions in terms of different values of two parameters for a system of conformable-type fractional differential equations with the p-Laplacian operator is obtained via Guo-Krasnosel’skii fixed point theorem.

scholarly journals Maximal and minimal iterative positive solutions for singular infinite-point p-Laplacian fractional differential equations

2018 ◽  
Vol 23 (6) ◽  
pp. 851-865 ◽  
Author(s):  
Limin Guo ◽  
Lishan Liub
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Green’S Function ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Green's Function ◽  
Fractional Differential Equations ◽  
Iterative Schemes ◽  
Infinite Point ◽  
Fractional Differential

The existence of maximal and minimal positive solutions for singular infinite-point p-Laplacian fractional differential equation is investigated in this paper. Green's function is derived, and some properties of Green's function are obtained. Based upon these properties of Green's function, the existence of maximal and minimal positive solutions is obtained, and iterative schemes are established for approximating the maximal and minimal positive solutions.

Sign in / Sign up

Export Citation Format

Share Document