scholarly journals Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Xiaoling Han ◽  
Hongliang Gao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Eigenvalue Problems ◽  
Positive Parameter ◽  
Nonlinear Eigenvalue Problems ◽  
Fractional Differential ◽  
The Fixed Point Theorem ◽  
Nonlinear Eigenvalue

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equationD0+αu(t)+λa(t)f(t,u(t))=0,  0<t<1,  u(0)=0,  u(1)=Σi=1∞αiu(ξi)are considered, where1<α≤2is a real number,λis a positive parameter,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),αi∈[0,∞)withΣi=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,∞),[0,∞)).

scholarly journals Existence of Positive Solutions for Fractional Differential Equation with Nonlocal Boundary Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Hongliang Gao ◽  
Xiaoling Han
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

By using the fixed point theorem, existence of positive solutions for fractional differential equation with nonlocal boundary conditionD0+αu(t)+a(t)f(t,u(t))=0,0<t<1,u(0)=0,u(1)=∑i=1∞αiu(ξi)is considered, where1<α≤2is a real number,D0+αis the standard Riemann-Liouville differentiation, andξi∈(0,1),  αi∈[0,∞)with∑i=1∞αiξiα-1<1,a(t)∈C([0,1],[0,∞)),  f(t,u)∈C([0,1]×[0,∞),[0,∞)).

scholarly journals Existence and Nonexistence of Positive Solutions for Fractional Three-Point Boundary Value Problems with a Parameter

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Yunhong Li ◽  
Weihua Jiang
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Fractional Differential

In this work, we investigate the existence and nonexistence of positive solutions for p-Laplacian fractional differential equation with a parameter. On the basis of the properties of Green’s function and Guo-Krasnosel’skii fixed point theorem on cones, the existence and nonexistence of positive solutions are obtained for the boundary value problems. We also give some examples to illustrate the effectiveness of our main results.

Existence of positive solutions for systems of nonlinear fractional differential equation with p-Laplacian

2019 ◽  
Vol 13 (05) ◽  
pp. 2050089 ◽  
Author(s):  
S. Nageswara Rao ◽  
Meshari Alesemi
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Sufficient Conditions ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, we establish sufficient conditions for the existence of positive solutions for a system of nonlinear fractional [Formula: see text]-Laplacian boundary value problems under different combinations of superlinearity and sublinearity of the nonlinearities via the Guo–Krasnosel’skii fixed point theorem. Moreover, an example is given to illustrate our results.

Existence of positive solutions for a class of fractional differential equation systems with multi-point boundary conditions

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohammad Hussian Akrami ◽  
Gholam Hussian Erjaee
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Existence Of Solutions ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential ◽  
The Fixed Point Theorem

AbstractIn this article, we study the existence of positive solutions of a multi-point boundary value problem for some system of fractional differential equations. The fixed point theorem on cones will be applied to demonstrate the existence of solutions for this system. At the end, an example shows the application of the main results.

The Existence of Positive Solutions for Boundary Value Problems of Fractional Differential Equation

2014 ◽  
Vol 711 ◽  
pp. 303-307 ◽  
Author(s):  
Jie Gao
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

In this paper, by using Leggett-Williams fixed point theorem, we will study the existence of positive solutions for a class of multi-point boundary value problems of fractional differential equation on infinite interval.

scholarly journals Existence and Uniqueness of Positive Solutions for Singular Nonlinear Fractional Differential Equation via Mixed Monotone Operator Method

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Tian Wang ◽  
Zhaocai Hao
Keyword(s):  
Differential Equation ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Operator Method ◽  
Mixed Monotone Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Singular Fractional Differential Equations ◽  
Fractional Differential ◽  
The Fixed Point Theorem

In this article, we discuss the existence and uniqueness of positive solution for a class of singular fractional differential equations, where the nonlinear term contains fractional derivative and an operator. By applying the fixed point theorem in cone, we get the existence and uniqueness of positive solutions for the fractional differential equation. Moreover, we give an example to demonstrate our main result.

scholarly journals Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Jinhua Wang ◽  
Hongjun Xiang ◽  
ZhiGang Liu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Boundary Value ◽  
Laplacian Operator ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Multiplicity ◽  
Fractional Differential

We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+ρu(t))=0,0<t<1,u(0)=u′(1)=0,u′′(0)=0,D0+αu(t)|t=0=0, where0<γ<1,2<α<3,0<ρ⩽1,D0+αdenotes the Caputo derivative, andf:[0,1]×[0,+∞)×R→[0,+∞)is continuous function,ϕp(s)=|s|p-2s,p>1,  (ϕp)-1=ϕq,  1/p+1/q=1. By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained. Finally, an example is given to show the effectiveness of our works.

scholarly journals Solutions for impulsive fractional pantograph differential equation via generalized anti-periodic boundary condition

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Idris Ahmed ◽  
Poom Kumam ◽  
Jamilu Abubakar ◽  
Piyachat Borisut ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fixed Point ◽  
Fractional Differential Equation ◽  
Existence And Uniqueness ◽  
Periodic Boundary Condition ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Uniqueness Of The Solution ◽  
Fractional Differential

Abstract This study investigates the solutions of an impulsive fractional differential equation incorporated with a pantograph. This work extends and improves some results of the impulsive fractional differential equation. A differential equation of an impulsive fractional pantograph with a more general anti-periodic boundary condition is proposed. By employing the well-known fixed point theorems of Banach and Krasnoselskii, the existence and uniqueness of the solution of the proposed problem are established. Furthermore, two examples are presented to support our theoretical analysis.

Sign in / Sign up

Export Citation Format

Share Document