scholarly journals The Green's function for Caputo fractional boundary value problem with a convection term

2022 ◽  
Vol 7 (4) ◽  
pp. 4887-4897
Author(s):  
Youyu Wang ◽  
◽  
Xianfei Li ◽  
Yue Huang
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Green's Function ◽  
Operator Theory ◽  
Fractional Boundary Value Problem ◽  
Convection Term ◽  
New Ideas ◽  
Sturm Liouville ◽  
Fractional Differential

<abstract><p>By using the operator theory, we establish the Green's function for Caputo fractional differential equation under Sturm-Liouville boundary conditions. The results are new, the method used in this paper will provide some new ideas for the study of this kind of problems and easy to be generalized to solving other problems.</p></abstract>

scholarly journals Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.

scholarly journals Existence of nonnegative solutions for a nonlinear fractional boundary value problem

2018 ◽  
Vol 1 (1) ◽  
pp. 56-80
Author(s):  
Assia Guezane-Lakoud ◽  
Kheireddine Belakroum
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Fractional Differential Equation ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Alternative ◽  
Nonnegative Solutions ◽  
Fractional Differential

AbstractThis paper deals with the existence of solutions for a class of boundary value problem (BVP) of fractional differential equation with three point conditions via Leray-Schauder nonlinear alternative. Moreover, the existence of nonnegative solutions is discussed.

scholarly journals Maximal and minimal iterative positive solutions for $ p $-Laplacian Hadamard fractional differential equations with the derivative term contained in the nonlinear term

2021 ◽  
Vol 6 (11) ◽  
pp. 12583-12598
Author(s):  
Limin Guo ◽  
◽  
Lishan Liu ◽  
Ying Wang ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Nonlinear Term ◽  
Iterative Schemes ◽  
Hadamard Fractional Differential Equations ◽  
Equation Boundary ◽  
Derivative Term ◽  
Fractional Differential

<abstract><p>In this paper, the maximal and minimal iterative positive solutions are investigated for a singular Hadamard fractional differential equation boundary value problem with a boundary condition involving values at infinite number of points. Green's function is deduced and some properties of Green's function are given. Based upon these properties, iterative schemes are established for approximating the maximal and minimal positive solutions.</p></abstract>

scholarly journals Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation

2007 ◽  
Vol 2007 ◽  
pp. 1-8 ◽  
Author(s):  
Moustafa El-Shahed
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Existence And Nonexistence ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem:D0+αu(t)+λa(t) f(u(t))=0, 0<t<1, u(0)=u′(0)=u′(1)=0,where2<α<3is a real number andD0+αis the standard Riemann-Liouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is also given to illustrate the main results.

scholarly journals A New Proof for Lyapunov-Type Inequality on the Fractional Boundary Value Problem

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 29
Author(s):  
Yumei Zou ◽  
Xin Zhang ◽  
Hongyu Li
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Green's Function ◽  
Boundary Value ◽  
Type Inequality ◽  
Fractional Boundary Value Problem ◽  
Lyapunov Type Inequality ◽  
Fractional Boundary Value Problems

In this article, some new Lyapunov-type inequalities for a class of fractional boundary value problems are established by use of the nonsymmetry property of Green’s function corresponding to appropriate boundary conditions.

scholarly journals Solution of Ordinary Differential Equation Using Green's Function & Sturm - Liouville Problem

2019 ◽  
pp. 241-244
Author(s):  
S. Angel Auxzaline Mary ◽  
T. Ramesh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Initial Value Problem ◽  
Series Representation ◽  
Liouville Problem ◽  
Initial Value ◽  
Sturm Liouville

In this paper, we describe Green's function to determine the importance of this function, i.e. Boundary & Initial Value problem, Sturm-Liouville Problem. Along with the series representation of Green's Function.

scholarly journals Solution of Inhomogeneous Fractional Differential Equations with Polynomial Coefficients in Terms of the Green’s Function, in Nonstandard Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1944
Author(s):  
Tohru Morita ◽  
Ken-ichi Sato
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Green’S Function ◽  
Fractional Differential Equation ◽  
Green's Function ◽  
Nonstandard Analysis ◽  
Polynomial Coefficients ◽  
Particular Solution ◽  
Fractional Differential ◽  
Detailed Derivation

Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the framework of distribution theory. In the present paper, a compact recipe in nonstandard analysis is presented, which is applicable to an inhomogeneous ordinary and also fractional differential equation with polynomial coefficients. The recipe consists of three theorems, each of which provides the particular solution of a differential equation for an inhomogeneous term, satisfying one of three conditions. The detailed derivation of the applications of these theorems is given for a simple fractional differential equation and an ordinary differential equation.

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