scholarly journals The Existence of Solutions for a Nonlinear Fractional Multi-Point Boundary Value Problem at Resonance

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoling Han ◽  
Ting Wang
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Existence Of Solution ◽  
At Resonance ◽  
Fractional Differential ◽  
Multipoint Boundary Value Problem

We discuss the existence of solution for a multipoint boundary value problem of fractional differential equation. An existence result is obtained with the use of the coincidence degree theory.

scholarly journals Solvability of a Third-Order Multipoint Boundary Value Problem at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zengji Du ◽  
Bensheng Zhao ◽  
Zhanbing Bai
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Third Order ◽  
Multipoint Boundary ◽  
At Resonance ◽  
Problem At Resonance ◽  
Multipoint Boundary Value Problem

We discuss a third-order multipoint boundary value problem under some appropriate resonance conditions. By using the coincidence degree theory, we establish the existence result of solutions. The emphasis here is that the dimension of the linear operator is equal to two. Our results supplement other results.

scholarly journals The Existence of Solutions for Four-Point Coupled Boundary Value Problems of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yumei Zou ◽  
Lishan Liu ◽  
Yujun Cui
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Existence Theorems ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
At Resonance ◽  
Fractional Differential

A four-point coupled boundary value problem of fractional differential equations is studied. Based on Mawhin’s coincidence degree theory, some existence theorems are obtained in the case of resonance.

scholarly journals Existence of Solutions for Two-Point Boundary Value Problem of Fractional Differential Equations at Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lei Hu ◽  
Shuqin Zhang ◽  
Ailing Shi
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Fractional Differential

We establish the existence results for two-point boundary value problem of fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results.

scholarly journals On a class of second-order impulsive boundary value problem at resonance

2006 ◽  
Vol 2006 ◽  
pp. 1-11
Author(s):  
Guolan Cai ◽  
Zengji Du ◽  
Weigao Ge
Keyword(s):  
Boundary Value Problem ◽  
Existence Result ◽  
Boundary Value ◽  
General Theorem ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Point Boundary ◽  
At Resonance ◽  
Impulsive Boundary Value Problem ◽  
Problem At Resonance

We consider the following impulsive boundary value problem,x″(t)=f(t,x,x′),t∈J\{t1,t2,…,tk},Δx(ti)=Ii(x(ti),x′(ti)),Δx′(ti)=Ji(x(ti),x′(ti)),i=1,2,…,k,x(0)=(0),x′(1)=∑j=1m−2αjx′(ηj). By using the coincidence degree theory, a general theorem concerning the problem is given. Moreover, we get a concrete existence result which can be applied more conveniently than recent results. Our results extend some work concerning the usualm-point boundary value problem at resonance without impulses.

scholarly journals The Existence of Solutions for a Fractional 2m-Point Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Gang Wang ◽  
Wenbin Liu ◽  
Jinyun Yang ◽  
Sinian Zhu ◽  
Ting Zheng
Keyword(s):  
Boundary Value Problem ◽  
Fractional Integral ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Fractional Boundary Value Problem ◽  
Point Boundary ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

By using the coincidence degree theory, we consider the following 2m-point boundary value problem for fractional differential equationD0+αut=ft,ut,D0+α-1ut,D0+α-2ut+et,0<t<1,I0+3-αut|t=0=0,D0+α-2u1=∑i=1m-2aiD0+α-2uξi,u1=∑i=1m-2biuηi,where2<α≤3,D0+αandI0+αare the standard Riemann-Liouville fractional derivative and fractional integral, respectively. A new result on the existence of solutions for above fractional boundary value problem is obtained.

PERIODIC BOUNDARY VALUE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATION

2012 ◽  
Vol 23 (10) ◽  
pp. 1250100 ◽  
Author(s):  
ZHIGANG HU ◽  
WENBIN LIU ◽  
WENJUAN RUI
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Periodic Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Periodic Boundary Value Problem ◽  
Fractional Differential

In this paper, by using the coincidence degree theory, we consider periodic boundary value problem for fractional differential equation. A new result on the existence of solutions for above fractional boundary value problem is obtained.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

scholarly journals On a fractional-order p-Laplacian boundary value problem at resonance on the half-line with two dimensional kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
O. F. Imaga ◽  
S. A. Iyase
Keyword(s):  
Differential Operator ◽  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Half Line ◽  
At Resonance ◽  
Fractional Differential Operator ◽  
Fractional Differential ◽  
Problem At Resonance

AbstractIn this work, we consider the solvability of a fractional-order p-Laplacian boundary value problem on the half-line where the fractional differential operator is nonlinear and has a kernel dimension equal to two. Due to the nonlinearity of the fractional differential operator, the Ge and Ren extension of Mawhin’s coincidence degree theory is applied to obtain existence results for the boundary value problem at resonance. Two examples are used to validate the established results.

scholarly journals On resonant mixed Caputo fractional differential equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Assia Guezane-Lakoud ◽  
Adem Kılıçman
Keyword(s):  
Differential Equation ◽  
Fractional Derivatives ◽  
Existence Of Solutions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Caputo Fractional Derivatives ◽  
At Resonance ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
Problem At Resonance

Abstract The purpose of this study is to discuss the existence of solutions for a boundary value problem at resonance generated by a nonlinear differential equation involving both right and left Caputo fractional derivatives. The proofs of the existence of solutions are mainly based on Mawhin’s coincidence degree theory. We provide an example to illustrate the main result.

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