scholarly journals Solvability of a fractional boundary value problem with fractional derivative condition

2014 ◽  
Vol 3 (1) ◽  
pp. 39-48 ◽  
Author(s):  
A. Guezane-Lakoud ◽  
S. Bensebaa
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value ◽  
Fractional Boundary Value Problem

scholarly journals Iterative approximation of positive solutions for fractional boundary value problem on the half-line

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6177-6187 ◽  
Author(s):  
Mourad Chamekh ◽  
Abdeljabbar Ghanmi ◽  
Samah Horrigue
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Boundary Value ◽  
The Other ◽  
Fractional Boundary Value Problem ◽  
Iterative Approximation ◽  
Derivative Operator ◽  
Liouville Fractional Derivative

In this paper, an iterative method is applied to solve some p-Laplacian boundary value problem involving Riemann-Liouville fractional derivative operator. More precisely, we establish the existence of two positive solutions. Moreover, we prove that these solutions are one maximal and the other is minimal. An example is presented to illustrate our main result. Finally, a numerical method to solve this problem is given.

scholarly journals On solutions of a class of three-point fractional boundary value problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhanbing Bai ◽  
Yu Cheng ◽  
Sujing Sun
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Existence Results ◽  
Conformable Fractional Derivative ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Fractional Boundary Value Problems

AbstractExistence results for the three-point fractional boundary value problem $$\begin{aligned}& D^{\alpha}x(t)= f \bigl(t, x(t), D^{\alpha-1} x(t) \bigr),\quad 0< t< 1, \\& x(0)=A, \qquad x(\eta)-x(1)=(\eta-1)B, \end{aligned}$$ Dαx(t)=f(t,x(t),Dα−1x(t)),0<t<1,x(0)=A,x(η)−x(1)=(η−1)B, are presented, where $A, B\in\mathbb{R}$A,B∈R, $0<\eta<1$0<η<1, $1<\alpha\leq2$1<α≤2. $D^{\alpha}x(t)$Dαx(t) is the conformable fractional derivative, and $f: [0, 1]\times\mathbb{R}^{2}\to\mathbb{R}$f:[0,1]×R2→R is continuous. The analysis is based on the nonlinear alternative of Leray–Schauder.

scholarly journals Hartman-Wintner-Type Inequality for a Fractional Boundary Value Problem via a Fractional Derivative with respect to Another Function

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Mohamed Jleli ◽  
Mokhtar Kirane ◽  
Bessem Samet
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Eigenvalue Problems ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem

We consider a fractional boundary value problem involving a fractional derivative with respect to a certain function g. A Hartman-Wintner-type inequality is obtained for such problem. Next, several Lyapunov-type inequalities are deduced for different choices of the function g. Moreover, some applications to eigenvalue problems are presented.

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