scholarly journals Functional Coupled Systems with Generalized Impulsive Conditions and Application to a SIRS-Type Model

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Feliz Minhós ◽  
Rui Carapinha
Keyword(s):  
Fixed Point Theory ◽  
Impulsive System ◽  
Point Theory ◽  
Coupled Systems ◽  
Impulsive Effects ◽  
Solution Technique ◽  
Type Model ◽  
Sirs Model ◽  
Lower And Upper Solution ◽  
Functional Boundary

In this paper, we consider a first-order coupled impulsive system of equations with functional boundary conditions, subject to the generalized impulsive effects. It is pointed out that this problem generalizes the classical boundary assumptions, allowing two-point or multipoint conditions, nonlocal and integrodifferential ones, or global arguments, as maxima or minima, among others. Our method is based on lower and upper solution technique together with the fixed point theory. The main theorem is applied to a SIRS model where to the best of our knowledge, for the first time, it includes impulsive effects combined with global, local, and the asymptotic behavior of the unknown functions.

scholarly journals First Order Coupled Systems With Functional and Periodic Boundary Conditions: Existence Results and Application to an SIRS Model

Axioms ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 23
Author(s):  
João Fialho ◽  
Feliz Minhós
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Coupled System ◽  
Periodic Boundary Conditions ◽  
Existence Results ◽  
Coupled Systems ◽  
First Order ◽  
Sirs Model ◽  
Functional Boundary ◽  
Functional Boundary Conditions

The results presented in this paper deal with the existence of solutions of a first order fully coupled system of three equations, and they are split in two parts: 1. Case with coupled functional boundary conditions, and 2. Case with periodic boundary conditions. Functional boundary conditions, which are becoming increasingly popular in the literature, as they generalize most of the classical cases and in addition can be used to tackle global conditions, such as maximum or minimum conditions. The arguments used are based on the Arzèla Ascoli theorem and Schauder’s fixed point theorem. The existence results are directly applied to an epidemic SIRS (Susceptible-Infectious-Recovered-Susceptible) model, with global boundary conditions.

scholarly journals New results and applications on the existence results for nonlinear coupled systems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Imran Talib ◽  
Thabet Abdeljawad ◽  
Manar A. Alqudah ◽  
Cemil Tunc ◽  
Rabia Ameen
Keyword(s):  
Fixed Point Theory ◽  
Coupled System ◽  
Point Theory ◽  
Coupled Systems ◽  
Lower And Upper Solutions ◽  
Nonlinear Boundary Value Problems ◽  
Fully Nonlinear ◽  
Nonlinear Coupled System ◽  
A Priori Bound ◽  
Special Cases

AbstractIn this manuscript, we study a certain classical second-order fully nonlinear coupled system with generalized nonlinear coupled boundary conditions satisfying the monotone assumptions. Our new results unify the existence criteria of certain linear and nonlinear boundary value problems (BVPs) that have been previously studied on a case-by-case basis; for example, Dirichlet and Neumann are special cases. The common feature is that the solution of each BVPs lies in a sector defined by well-ordered coupled lower and upper solutions. The tools we use are the coupled lower and upper solutions approach along with some results of fixed point theory. By means of the coupled lower and upper solutions approach, the considered BVPs are logically modified to new problems, known as modified BVPs. The solution of the modified BVPs leads to the solution of the original BVPs. In our case, we only require the Nagumo condition to get a priori bound on the derivatives of the solution function. Further, we extend the results presented in (Franco et al. in Extr. Math. 18(2):153–160, 2003; Franco et al. in Appl. Math. Comput. 153:793–802, 2004; Franco and O’Regan in Arch. Inequal. Appl. 1:423–430, 2003; Asif et al. in Bound. Value Probl. 2015:134, 2015). Finally, as an application, we consider the fully nonlinear coupled mass-spring model.

scholarly journals Existence and uniqueness of positive solutions for nonlinear fractional mixed problems

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Alberto Cabada ◽  
Om Kalthoum Wanassi
Keyword(s):  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Mixed Boundary ◽  
Point Theory ◽  
Uniqueness Of Solutions ◽  
Nonlinear Part ◽  
Banach Contraction ◽  
Fractional Differential ◽  
Exhaustive Study ◽  
The Banach Contraction Principle

Abstract This paper is devoted to study the existence and uniqueness of solutions of a one parameter family of nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive study of the sign of the related Green’s function is carried out. Under suitable assumptions on the asymptotic behavior of the nonlinear part of the equation at zero and at infinity, and by application of the fixed point theory of compact operators defined in suitable cones, it is proved that there exists at least one solution of the considered problem. Moreover, the method of lower and upper solutions is developed and the existence of solutions is deduced by a combination of both techniques. In particular cases, the Banach contraction principle is used to ensure the uniqueness of solutions.

scholarly journals On a nonlinear system of Riemann-Liouville fractional differential equations with semi-coupled integro-multipoint boundary conditions

2021 ◽  
Vol 19 (1) ◽  
pp. 760-772
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Badrah Alghamdi ◽  
Sotiris K. Ntouyas
Keyword(s):  
Nonlinear System ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Fractional Differential Equations ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Numerical Examples ◽  
Multipoint Boundary ◽  
Multipoint Boundary Conditions ◽  
Fractional Differential

Abstract We study a nonlinear system of Riemann-Liouville fractional differential equations equipped with nonseparated semi-coupled integro-multipoint boundary conditions. We make use of the tools of the fixed-point theory to obtain the desired results, which are well-supported with numerical examples.

Graphical structure of extended b-metric spaces: an application to the transverse oscillations of a homogeneous bar

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mudasir Younis ◽  
Deepak Singh ◽  
Ishak Altun ◽  
Varsha Chauhan
Keyword(s):  
Metric Spaces ◽  
Fixed Point Theory ◽  
Directed Graphs ◽  
Point Theory ◽  
Graph Structure ◽  
Open Ball ◽  
Open Problems ◽  
Graphical Structure ◽  
State Of Art ◽  
Transverse Oscillations

Abstract The purpose of this article is to present the notion of graphical extended b-metric spaces, blending the concepts of graph theory and metric fixed point theory. We discuss the structure of an open ball of the new proposed space and elaborate on the newly introduced ideas in a novel way by portraying suitably directed graphs. We also provide some examples in graph structure to show that our results are sharp as compared to the results in the existing state-of-art. Furthermore, an application to the transverse oscillations of a homogeneous bar is entrusted to affirm the applicability of the established results. Additionally, we evoke some open problems for enthusiastic readers for the future aspects of the study.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

Modeling of assembly systems with complex structures for throughput analysis during transients

2019 ◽  
Vol 39 (2) ◽  
pp. 262-271
Author(s):  
Yukan Hou ◽  
Yuan Li ◽  
Yuntian Ge ◽  
Jie Zhang ◽  
Shoushan Jiang
Keyword(s):  
Steady State ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Assembly Systems ◽  
Complex Structures ◽  
Throughput Performance ◽  
Throughput Analysis ◽  
Content Type ◽  
Serial Production Lines ◽  
Transient And Steady State

Purpose The purpose of this paper is to present an analytical method for throughput analysis of assembly systems with complex structures during transients. Design/methodology/approach Among the existing studies on the performance evaluation of assembly systems, most focus on the system performance in steady state. Inspired by the transient analysis of serial production lines, the state transition matrix is derived considering the characteristics of merging structure in assembly systems. The system behavior during transients is described by an ergodic Markov chain, with the states being the occupancy of all buffers. The dynamic model for the throughput analysis is solved using the fixed-point theory. Findings This method can be used to predict and evaluate the throughput performance of assembly systems in both transient and steady state. By comparing the model calculation results with the simulation results, this method is proved to be accurate. Originality/value This proposed modeling method can depict the throughput performance of assembly systems in both transient and steady state, whereas most exiting methods can be used for only steady-state analysis. In addition, this method shows the potential for the analysis of complex structured assembly systems owing to the low computational complexity.

scholarly journals A new method in fixed point theory

1960 ◽  
Vol 34 (1) ◽  
pp. 1-16 ◽  
Author(s):  
Richard G. Swan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Point Theory ◽  
New Method
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