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 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 The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Weihua Jiang ◽  
Jiqing Qiu ◽  
Weiwei Guo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Eigenvalue Problems ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Generalized Boundary Conditions

We investigate the existence of at least two positive solutions to eigenvalue problems of fractional differential equations with sign changing nonlinearities in more generalized boundary conditions. Our analysis relies on the Avery-Peterson fixed point theorem in a cone. Some examples are given for the illustration of main results.

scholarly journals Positive solutions to advanced fractional differential equations with nonlocal boundary conditions

2015 ◽  
Vol 9 (2) ◽  
pp. 209-220 ◽  
Author(s):  
Tadeusz Jankowski
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Nonlocal Boundary Conditions ◽  
Multiple Positive Solutions ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

In this paper, we study the existence of positive solutions for a class of higher order fractional differential equations with advanced arguments and boundary value problems involving Stieltjes integral conditions. The fixed point theorem due to Avery-Peterson is used to obtain sufficient conditions for the existence of multiple positive solutions. Certain of our results improve on recent work in the literature.

Existence of Positive Solutions to the Singular Initial Value Problems of Fractional Differential Equations

2011 ◽  
Vol 403-408 ◽  
pp. 563-569
Author(s):  
Qiu Ping Li ◽  
Shu Rong Sun ◽  
Zhen Lai Han ◽  
Yi Ge Zhao
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Initial Value Problem ◽  
Sufficient Conditions ◽  
Initial Value ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

In this paper, we consider the existence of positive solutions for the initial value problem of nonlinear fractional differential equations where and is the Riemann–Liouville fractional derivative. By using the Nonlinear Alternative of Leray and Schauder theorem, some sufficient conditions for the existence of at least one positive solution for the initial value problem are established.

scholarly journals Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving Riemann-Stieltjes Integrals

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Theorems ◽  
Integral Boundary ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
Integral Boundary Value Problems

We consider the existence of positive solutions for a class of nonlinear integral boundary value problems for fractional differential equations. By using some fixed point theorems, the existence and multiplicity results of positive solutions are obtained. The results obtained in this paper improve and generalize some well-known results.

Positive solutions for a system of nonlocal fractional boundary value problems

2013 ◽  
Vol 16 (4) ◽  
Author(s):  
Johnny Henderson ◽  
Rodica Luca
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Existence Results ◽  
Hammerstein Integral Equations ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

AbstractWe investigate the existence of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to multipoint boundary conditions. Existence results for systems of nonlinear Hammerstein integral equations are also presented. Some nontrivial examples are included.

scholarly journals Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Youzheng Ding ◽  
Jiqiang Jiang ◽  
Donal O’Regan ◽  
Jiafa Xu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Fractional Differential Equations ◽  
Fixed Point Index ◽  
Nonnegative Matrices ◽  
Point Index ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we use the fixed-point index and nonnegative matrices to study the existence of positive solutions for a system of Hadamard-type fractional differential equations with semipositone nonlinearities.

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