Lyapunov-type inequalities for nonlinear fractional differential equation with Hilfer fractional derivative under multi-point boundary conditions

2018 ◽  
Vol 21 (3) ◽  
pp. 833-843 ◽  
Author(s):  
Youyu Wang ◽  
Qichao Wang
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Point Boundary ◽  
Hilfer Fractional Derivative ◽  
Nonlinear Fractional Differential Equation ◽  
Early Results ◽  
Fractional Differential ◽  
Fractional Boundary Value Problems

Abstract In this work, we establish Lyapunov-type inequalities for the fractional boundary value problems with Hilfer fractional derivative under multi-point boundary conditions, the results are new and generalize and improve some early results in the literature.

scholarly journals Existence Results for a Coupled System of Nonlinear Fractional Differential Equation with Four-Point Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
M. Gaber ◽  
M. G. Brikaa
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Existence Result ◽  
Coupled System ◽  
Existence Results ◽  
Point Boundary ◽  
Nonlinear Fractional Differential Equation ◽  
Fractional Differential

This paper studies a coupled system of nonlinear fractional differential equation with four-point boundary conditions. Applying the Schauder fixed-point theorem, an existence result is proved for the following system: , , , , , , , , where satisfy certain conditions.

scholarly journals Three-Point Boundary Value Problems for Conformable Fractional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
H. Batarfi ◽  
Jorge Losada ◽  
Juan J. Nieto ◽  
W. Shammakh
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Fractional Differential Equations ◽  
Linear Problem ◽  
Point Boundary ◽  
Fractional Differential ◽  
Novel Concept

We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. We first obtain Green's function for the linear problem and then we study the nonlinear differential equation.

scholarly journals Implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative

2021 ◽  
Vol 2 (1) ◽  
pp. 62-71
Author(s):  
Saleh Redhwan ◽  
Sadikali L. Shaikh
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Derivative ◽  
Fractional Differential Equation ◽  
Hilfer Fractional Derivative ◽  
Multipoint Boundary ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

This article deals with a nonlinear implicit fractional differential equation with nonlocal integral-multipoint boundary conditions in the frame of Hilfer fractional derivative. The existence and uniqueness results are obtained by using the fixed point theorems of Krasnoselskii and Banach. Further, to demonstrate the effectiveness of the main results, suitable examples are granted.

scholarly journals Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Min Li ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Method ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Zero Function ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper.

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