scholarly journals Monotone Iterative Schemes for Positive Solutions of a Fractional q -Difference Equation with Integral Boundary Conditions on the Half-Line

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Min Jiang ◽  
Rengang Huang
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Integral Boundary Conditions ◽  
Half Line ◽  
Monotone Iterative Method ◽  
Integral Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative ◽  
Nonlocal Integral Boundary Conditions ◽  
The Green Function

In this paper, we study the boundary value problem of a fractional q -difference equation with nonlocal integral boundary conditions on the half-line. Using the properties of the Green function and monotone iterative method, the extremal solutions are obtained. Finally, an example is presented to illustrate our main results.

A Fractional q$q$-difference Equation with Integral Boundary Conditions and Comparison Theorem

2017 ◽  
Vol 18 (7-8) ◽  
pp. 575-583 ◽  
Author(s):  
Jing Ren ◽  
Chengbo Zhai
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Comparison Theorem ◽  
Solution Method ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Technique ◽  
Extremal Solutions ◽  
Integral Boundary ◽  
Iterative Schemes ◽  
Monotone Iterative

AbstractIn this article, we mainly prove the existence of extremal solutions for a fractional $q$-difference equation involving Riemann–Lioville type fractional derivative with integral boundary conditions. A comparison theorem under weak conditions is also build, and then we apply the comparison theorem, monotone iterative technique and lower–upper solution method to prove the existence of extremal solutions. Moreover, we can construct two iterative schemes approximating the extremal solutions of the fractional $q$-difference equation with integral boundary conditions. In the last section, a simple example is presented to illustrate the main result.

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.

scholarly journals Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1905
Author(s):  
Athasit Wongcharoen ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Differential Inclusions ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Fractional Differential ◽  
Nonlocal Integral Boundary Conditions

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

scholarly journals A Study of Nonlinear Fractionalq-Difference Equations with Nonlocal Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Hana Al-Hutami
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Nonlocal Integral Boundary Conditions

This paper is concerned with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractionalq-difference equations with nonlocal integral boundary conditions. The existence results are obtained by applying some well-known fixed point theorems and illustrated with examples.

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