scholarly journals A MAXIMUM PRINCIPLE FOR A FRACTIONAL BOUNDARY VALUE PROBLEM WITH CONVECTION TERM AND APPLICATIONS

2018 ◽  
Vol 24 (1) ◽  
pp. 62-71 ◽  
Author(s):  
Mohammed Al-Refai ◽  
Kamal Pal
Keyword(s):  
Maximum Principle ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Boundary Value ◽  
Extreme Points ◽  
Uniqueness Result ◽  
Fractional Boundary Value Problem ◽  
Convection Term ◽  
Linear And Nonlinear

We consider a fractional boundary value problem with Caputo-Fabrizio fractional derivative of order 1 < α < 2 We prove a maximum principle for a general linear fractional boundary value problem. The proof is based on an estimate of the fractional derivative at extreme points and under certain assumption on the boundary conditions. A prior norm estimate of solutions of the linear fractional boundary value problem and a uniqueness result of the nonlinear problem have been established. Several comparison principles are derived for the linear and nonlinear fractional problems.

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 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.

Lyapunov-type inequality for an anti-periodic fractional boundary value problem

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Rui A. C. Ferreira
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Boundary Value ◽  
Type Inequality ◽  
Periodic Boundary Conditions ◽  
Fractional Boundary Value Problem ◽  
Research Directions ◽  
Lyapunov Type Inequality

AbstractIn this note we present a Lyapunov-type inequality for a fractional boundary value problem with anti-periodic boundary conditions, that we show to be a generalization of a classical one. Moreover, we address the issue of further research directions for such type of inequalities.

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