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 nonnegative solutions for a nonlinear fractional boundary value problem

2018 ◽  
Vol 1 (1) ◽  
pp. 56-80
Author(s):  
Assia Guezane-Lakoud ◽  
Kheireddine Belakroum
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Nonnegative Solutions ◽  
Fractional Differential

AbstractThis paper deals with the existence of solutions for a class of boundary value problem (BVP) of fractional differential equation with three point conditions via Leray-Schauder nonlinear alternative. Moreover, the existence of nonnegative solutions is discussed.

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 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.

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 Nontrivial Solutions of a Fully Fourth-Order Periodic Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Haitong Li ◽  
Minghe Pei ◽  
Libo Wang
Keyword(s):  
Boundary Value Problem ◽  
Fourth Order ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Periodic Boundary Value Problem ◽  
Coincidence Degree Theory ◽  
Nontrivial Solutions ◽  
Carathéodory Conditions

We investigate the solvability of a fully fourth-order periodic boundary value problem of the formx(4)=f(t,x,x′,x′′,x′′′),  x(i)(0)=x(i)(T),      i=0,1,2,3,wheref:[0,T]×R4→Rsatisfies Carathéodory conditions. By using the coincidence degree theory, the existence of nontrivial solutions is obtained. Meanwhile, as applications, some examples are given to illustrate our results.

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