scholarly journals Nonlocal q-Symmetric Integral Boundary Value Problem for Sequential q-Symmetric Integrodifference Equations

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 218 ◽  
Author(s):  
Rujira Ouncharoen ◽  
Nichaphat Patanarapeelert ◽  
Thanin Sitthiwirattham
Keyword(s):  
Boundary Value Problem ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Integrodifference Equation ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Symmetric Integral

In this paper, we prove the sufficient conditions for the existence results of a solution of a nonlocal q-symmetric integral boundary value problem for a sequential q-symmetric integrodifference equation by using the Banach’s contraction mapping principle and Krasnoselskii’s fixed point theorem. Some examples are also presented to illustrate our results.

scholarly journals Positive Solutions of a Nonlinear Fourth-order Integral Boundary Value Problem

2016 ◽  
Vol 54 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Slimane Benaicha ◽  
Faouzi Haddouchi
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Integral Condition ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Existence Of Positive Solutions

Abstract In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii’s fixed point theorem on cones, sufficient conditions for the existence of at least one positive solutions are obtained.

scholarly journals On a Nonlocal Multipoint and Integral Boundary Value Problem of Nonlinear Fractional Integrodifferential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Lahcen Ibnelazyz ◽  
Karim Guida ◽  
Said Melliani ◽  
Khalid Hilal
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Integrodifferential Equations ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Integral Boundary Value Problem ◽  
Uniqueness Results

The aim of this paper is to give the existence as well as the uniqueness results for a multipoint nonlocal integral boundary value problem of nonlinear sequential fractional integrodifferential equations. First of all, we give some preliminaries and notations that are necessary for the understanding of the manuscript; second of all, we show the existence and uniqueness of the solution by means of the fixed point theory, namely, Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Last, but not least, we give two examples to illustrate the results.

scholarly journals Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractionalq-Derivatives Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yulin Zhao ◽  
Guobing Ye ◽  
Haibo Chen
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Index Theorem ◽  
Multiple Positive Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Fixed Point Index Theorem

By using the fixed point index theorem, this paper investigates a class of singular semipositone integral boundary value problem for fractionalq-derivatives equations and obtains sufficient conditions for the existence of at least two and at least three positive solutions. Further, an example is given to illustrate the applications of our main results.

scholarly journals Boundary value problem solution existence for linear integro-differential equations with many delays

2018 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
I.M. Cherevko ◽  
A.B. Dorosh
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Problem Solution ◽  
Existence Of A Solution ◽  
Variable Delays

For the study of boundary value problems for delay differential equations, the contraction mapping principle and topological methods are used to obtain sufficient conditions for the existence of a solution of differential equations with a constant delay. In this paper, the ideas of the contraction mapping principle are used to obtain sufficient conditions for the existence of a solution of linear boundary value problems for integro-differential equations with many variable delays. Smoothness properties of the solutions of such equations are studied and the definition of the boundary value problem solution is proposed. Properties of the variable delays are analyzed and functional space is obtained in which the boundary value problem is equivalent to a special integral equation. Sufficient, simple for practical verification coefficient conditions for the original equation are found under which there exists a unique solution of the boundary value problem.

scholarly journals Existence results for nonlinear impulsive qk-integral boundary value problems

2016 ◽  
Vol 99 (113) ◽  
pp. 227-235 ◽  
Author(s):  
Lihong Zhang ◽  
Bashir Ahmad ◽  
Guotao Wang
Keyword(s):  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Degree Theory ◽  
Contraction Mapping Principle ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Integral Boundary Value Problem ◽  
Integral Boundary Value Problems

We investigate a nonlinear impulsive qk-integral boundary value problem by means of Leray-Schauder degree theory and contraction mapping principle. The conditions ensuring the existence and uniqueness of solutions for the problem are presented. An illustrative example is discussed.

scholarly journals Discrete fractional order two-point boundary value problem with some relevant physical applications

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
A. George Maria Selvam ◽  
Jehad Alzabut ◽  
R. Dhineshbabu ◽  
S. Rashid ◽  
M. Rehman
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Contraction Mapping ◽  
Boundary Value ◽  
Contraction Mapping Principle ◽  
Difference Operators ◽  
Point Boundary ◽  
Uniqueness Of Solutions ◽  
Fractional Difference ◽  
Rassias Stability

Abstract The results reported in this paper are concerned with the existence and uniqueness of solutions of discrete fractional order two-point boundary value problem. The results are developed by employing the properties of Caputo and Riemann–Liouville fractional difference operators, the contraction mapping principle and the Brouwer fixed point theorem. Furthermore, the conditions for Hyers–Ulam stability and Hyers–Ulam–Rassias stability of the proposed discrete fractional boundary value problem are established. The applicability of the theoretical findings has been demonstrated with relevant practical examples. The analysis of the considered mathematical models is illustrated by figures and presented in tabular forms. The results are compared and the occurrence of overlapping/non-overlapping has been discussed.

scholarly journals Sequential Derivatives of Nonlinearq-Difference Equations with Three-Pointq-Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Nittaya Pongarm ◽  
Suphawat Asawasamrit ◽  
Jessada Tariboon
Keyword(s):  
Boundary Conditions ◽  
Difference Equations ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Degree Theory ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Quantum Numbers ◽  
Derivatives Of

This paper studies sufficient conditions for the existence of solutions to the problem of sequential derivatives of nonlinearq-difference equations with three-pointq-integral boundary conditions. Our results are concerned with several quantum numbers of derivatives and integrals. By using Banach's contraction mapping, Krasnoselskii's fixed-point theorem, and Leray-Schauder degree theory, some new existence results are obtained. Two examples illustrate our results.

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