scholarly journals On a Multipoint Boundary Value Problem for a Fractional Order Differential Inclusion on an Infinite Interval

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nemat Nyamoradi ◽  
Dumitru Baleanu ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fractional Order ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Multipoint Boundary ◽  
Liouville Fractional Derivative ◽  
The Right ◽  
Multipoint Boundary Value Problem

We investigate the existence of solutions for the following multipoint boundary value problem of a fractional order differential inclusionD0+αut+Ft,ut,u′t∋0,0<t<+∞,u0=u′0=0,Dα-1u+∞-∑i=1m-2‍βiuξi=0, whereD0+αis the standard Riemann-Liouville fractional derivative,2<α<3,0<ξ1<ξ2<⋯<ξm-2<+∞, satisfies0<∑i=1m-2‍βiξiα-1<Γ(α),  and  F:[0,+∞)×ℝ×ℝ→𝒫(ℝ)is a set-valued map. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or nonconvex values.

On a fractional differential inclusion with “maxima”

2016 ◽  
Vol 19 (5) ◽  
Author(s):  
Aurelian Cernea
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Results ◽  
Fractional Differential Inclusion ◽  
Right Hand ◽  
Fractional Differential ◽  
The Right

Abstract We study a boundary value problem associated to a fractional differential inclusion with “maxima”. Several existence results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

scholarly journals Multiple Positive Solutions to Multipoint Boundary Value Problem for a System of Second-Order Nonlinear Semipositone Differential Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Gang Wu ◽  
Longsuo Li ◽  
Xinrong Cong ◽  
Xiufeng Miao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Time Scales ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Dynamic Equations ◽  
Multiple Positive Solutions ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problem

We study a system of second-order dynamic equations on time scales(p1u1∇)Δ(t)-q1(t)u1(t)+λf1(t,u1(t),u2(t))=0,t∈(t1,tn),(p2u2∇)Δ(t)-q2(t)u2(t)+λf2(t,u1(t),u2(t))=0, satisfying four kinds of different multipoint boundary value conditions,fiis continuous and semipositone. We derive an interval ofλsuch that anyλlying in this interval, the semipositone coupled boundary value problem has multiple positive solutions. The arguments are based upon fixed-point theorems in a cone.

scholarly journals Existence of Solutions for Riemann-Liouville Fractional Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Wenzhe Xie ◽  
Jing Xiao ◽  
Zhiguo Luo
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extreme Points ◽  
Fractional Boundary Value Problem ◽  
Liouville Fractional Derivative

By using the method of upper and lower solutions and fixed point theorems, the existence of solutions for a Riemann-Liouville fractional boundary value problem with the nonlinear term depending on fractional derivative of lower order is obtained under the classical Nagumo conditions. Also, some results concerning Riemann-Liouville fractional derivative at extreme points are established with weaker hypotheses, which improve some works in Al-Refai (2012). As applications, an example is presented to illustrate our main results.

scholarly journals Positive Solutions for Multipoint Boundary Value Problem of Fractional Differential Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Wenyong Zhong
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Liouville Fractional Derivative ◽  
Fractional Differential ◽  
Multiplicity Of Positive Solutions ◽  
Multipoint Boundary Value Problem

We study the existence and multiplicity of positive solutions for the fractionalm-point boundary value problemD0+αu(t)+f(t,u(t))=0,0<t<1,u(0)=u'(0)=0,u'(1)=∑i=1m-2aiu'(ξi), where2<α<3,D0+αis the standard Riemann-Liouville fractional derivative, andf:[0,1]×[0,∞)↦[0,∞)is continuous. Here,ai⩾0fori=1,…,m-2,0<ξ1<ξ2<⋯<ξm-2<1, andρ=∑i=1m-2aiξiα-2withρ<1. In light of some fixed point theorems, some existence and multiplicity results of positive solutions are obtained.

Existence of solutions for a second order boundary value problem with the Clarke subdifferential

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2763-2771 ◽  
Author(s):  
Dalila Azzam-Laouir ◽  
Samira Melit
Keyword(s):  
Boundary Value Problem ◽  
Differential Inclusion ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Clarke Subdifferential ◽  
Lipschitzian Function ◽  
The Clarke Subdifferential

In this paper, we prove a theorem on the existence of solutions for a second order differential inclusion governed by the Clarke subdifferential of a Lipschitzian function and by a mixed semicontinuous perturbation.

scholarly journals Positive Solutions for Resonant and Nonresonant Nonlinear Third-Order Multipoint Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Liu Yang ◽  
Chunfang Shen ◽  
Dapeng Xie
Keyword(s):  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Type Theorem ◽  
Third Order ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems ◽  
First Time ◽  
Multipoint Boundary Value Problem

Positive solutions for a kind of third-order multipoint boundary value problem under the nonresonant conditions and the resonant conditions are considered. In the nonresonant case, by using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions is obtained. In the resonant case, by using the Leggett-Williams norm-type theorem due to O’Regan and Zima, the existence result of at least one positive solution is established. It is remarkable to point out that it is the first time that the positive solution is considered for the third-order boundary value problem at resonance. Some examples are given to demonstrate the main results of the paper.

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