scholarly journals Nonlocal Neumann Boundary Value Problem for Fractional Symmetric Hahn Integrodifference Equations

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2303
Author(s):  
Thongchai Dumrongpokaphan ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Difference Operators ◽  
Banach Fixed Point Theorem ◽  
Integrodifference Equations ◽  
Integrodifference Equation ◽  
Neumann Boundary Value Problems

In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric Hahn integral of different orders. We employ Banach fixed point theorem and Schauder’s fixed point theorem to study the existence results of the problem.

scholarly journals Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type

2021 ◽  
Vol 26 (5) ◽  
pp. 914-927
Author(s):  
Sergey Smirnov
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Unique Solution ◽  
Point Theorem ◽  
Boundary Value ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Banach Fixed Point Theorem ◽  
Third Order

The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.

scholarly journals Boundary value problems for impulsive fractional differential equations in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (18) ◽  
pp. 5603-5616 ◽  
Author(s):  
Shuai Yang ◽  
Shuqin Zhang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Banach Spaces ◽  
Point Theorem ◽  
Boundary Value ◽  
Banach Fixed Point Theorem ◽  
Uniqueness Of Solutions ◽  
Impulsive Fractional Differential Equations ◽  
Fractional Differential

This paper is devoted to studying the existence and uniqueness of solutions to the boundary value problems for a impulsive fractional differential equation in Banach spaces. The arguments are based upon the methods of noncompact measure, Banach fixed point theorem and Krasnoselskii?s fixed point theorem. Some examples are given to demonstrate the application of our main results.

scholarly journals On Almost Automorphic Mild Solutions for Nonautonomous Stochastic Evolution Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jing Cui ◽  
Litan Yan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Banach Fixed Point Theorem ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Almost Automorphic ◽  
Composition Theorem

We consider a class of nonautonomous stochastic evolution equations in real separable Hilbert spaces. We establish a new composition theorem for square-mean almost automorphic functions under non-Lipschitz conditions. We apply this new composition theorem as well as intermediate space techniques, Krasnoselskii fixed point theorem, and Banach fixed point theorem to investigate the existence of square-mean almost automorphic mild solutions. Some known results are generalized and improved.

scholarly journals RETRACTED ARTICLE: Existence and uniqueness of solutions for the Schrödinger integrable boundary value problem

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Jianjie Wang ◽  
Ali Mai ◽  
Hong Wang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solutions ◽  
Linear Maps ◽  
Retracted Article

Abstract This paper is mainly devoted to the study of one kind of nonlinear Schrödinger differential equations. Under the integrable boundary value condition, the existence and uniqueness of the solutions of this equation are discussed by using new Riesz representations of linear maps and the Schrödinger fixed point theorem.

scholarly journals Multiplicity Result of Positive Solutions for Nonlinear Differential Equation of Fractional Order

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Yang Liu ◽  
Zhang Weiguo
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Order ◽  
Point Theorem ◽  
Boundary Value ◽  
Order Derivative ◽  
Fractional Order Derivative

We investigate the existence of multiple positive solutions for a class of boundary value problems of nonlinear differential equation with Caputo’s fractional order derivative. The existence results are obtained by means of the Avery-Peterson fixed point theorem. It should be point out that this is the first time that this fixed point theorem is used to deal with the boundary value problem of differential equations with fractional order derivative.

scholarly journals Existence results of ψ-Hilfer integro-differential equations with fractional order in Banach space

2020 ◽  
Vol 19 (1) ◽  
pp. 171-192
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Banach Fixed Point Theorem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Mönch Fixed Point Theorem

AbstractIn this article we present the existence and uniqueness results for fractional integro-differential equations with ψ-Hilfer fractional derivative. The reasoning is mainly based upon different types of classical fixed point theory such as the Mönch fixed point theorem and the Banach fixed point theorem. Furthermore, we discuss Eα -Ulam-Hyers stability of the presented problem. Also, we use the generalized Gronwall inequality with singularity to establish continuous dependence and uniqueness of the δ-approximate solution.

scholarly journals Uniqueness and Stability Results on Non-local Stochastic Random Impulsive Integro-Differential Equations

2021 ◽  
Vol 2 (3) ◽  
pp. 9-20
Author(s):  
VARSHINI S ◽  
BANUPRIYA K ◽  
RAMKUMAR K ◽  
RAVIKUMAR K
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Sufficient Conditions ◽  
Banach Fixed Point Theorem ◽  
Local Conditions ◽  
Non Local ◽  
Inequality Techniques ◽  
Stability Results

The paper is concerned with stochastic random impulsive integro-differential equations with non-local conditions. The sufficient conditions guarantees uniqueness of mild solution derived using Banach fixed point theorem. Stability of the solution is derived by incorporating Banach fixed point theorem with certain inequality techniques.

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