scholarly journals Analytical and numerical study for a fractional boundary value problem with a conformable fractional derivative of Caputo and its fractional integral

2020 ◽  
Vol 19 (2) ◽  
pp. 31-42
Author(s):  
M. Moumen Bekkouche ◽  
H. Guebbai
Keyword(s):  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Fractional Integral ◽  
Numerical Study ◽  
Boundary Value ◽  
Conformable Fractional Derivative ◽  
Fractional Boundary Value Problem

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 Lyapunov-Type Inequalities for a Conformable Fractional Boundary Value Problem of Order 3<α≤4

2019 ◽  
Vol 2019 ◽  
pp. 1-5 ◽  
Author(s):  
Imed Bachar ◽  
Hassan Eltayeb
Keyword(s):  
Continuous Function ◽  
Eigenvalue Problem ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Boundary Value ◽  
Conformable Fractional Derivative ◽  
Fractional Boundary Value Problem

We establish new Lyapunov-type inequalities for the following conformable fractional boundary value problem (BVP): Tαaut+q(t)u(t)=0,  a<t<b,  u(a)=u′(a)=u′′(a)=u′′(b)=0, where Tαa is the conformable fractional derivative of order α∈(3,4] and q is a real-valued continuous function. Some applications to the corresponding eigenvalue problem are discussed.

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 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 Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
A. Guezane-Lakoud ◽  
R. Khaldi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Fractional Integral ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Fractional Boundary Value Problem ◽  
Deviating Argument

This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

Sign in / Sign up

Export Citation Format

Share Document