scholarly journals A Sum Operator Method for the Existence and Uniqueness of Positive Solutions to a System of Nonlinear Fractional Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jing Wu ◽  
Tunhua Wu
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Iterative Scheme ◽  
Operator Method ◽  
Quadratic System ◽  
System Of Integral Equations ◽  
Fractional System

This paper is concerned with the existence and uniqueness of positive solutions for a Volterra nonlinear fractional system of integral equations. Our analysis relies on a fixed point theorem of a sum operator. The conditions for the existence and uniqueness of a positive solution to the system are established. Moreover, an iterative scheme is constructed for approximating the solution. The case of quadratic system of fractional integral equations is also considered.

scholarly journals Fixed Point Results for F-Contractions in Cone Metric Spaces over Topological Modules and Applications to Integral Equations

2021 ◽  
Vol 6 (1) ◽  
pp. 16
Author(s):  
Adrian Nicolae Branga
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Metric Spaces ◽  
Contractive Condition ◽  
Cone Metric Spaces ◽  
Fractional Integral Equation ◽  
Topological Modules ◽  
Cone Metric

In this paper, the concept of F-contraction was generalized for cone metric spaces over topological left modules and some fixed point results were obtained for self-mappings satisfying a contractive condition of this type. Some applications of the main result to the study of the existence and uniqueness of the solutions for certain types of integral equations were presented in the last part of the article, one of them being a fractional integral equation.

Solving a system of integral equations by using some tripled fixed point theorems

2020 ◽  
Vol 29 (1) ◽  
pp. 51-56
Author(s):  
MONICA LAURAN ◽  
ADINA POP
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
System Of Integral Equations ◽  
Tripled Fixed Point ◽  
Uniqueness Of A Solution ◽  
Theoretical Results

A tripled fixed point theorems in ordered metric spaces is used in order to prove the existence and uniqueness of a solution for a class of integral equations. The conditions of the theorem are much weaker than those existing in literature and the theorem is useful for solving some general problems. An example to illustrate our theoretical results is also given.

scholarly journals Global Existence of Solutions to a System of Integral Equations Related to an Epidemic Model

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Global Solutions ◽  
System Of Integral Equations ◽  
Global Existence Of Solutions

A system of integral equations related to an epidemic model is investigated. Namely, we derive sufficient conditions for the existence and uniqueness of global solutions to the considered system. The proof is based on Perov’s fixed point theorem and some integral inequalities.

scholarly journals Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 56 ◽  
Author(s):  
Qasim Mahmood ◽  
Abdullah Shoaib ◽  
Tahair Rasham ◽  
Muhammad Arshad
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Metric Space ◽  
Metric Spaces ◽  
Closed Ball ◽  
Multivalued Mappings ◽  
System Of Integral Equations ◽  
Contractive Mappings ◽  
The Family ◽  
Rational Type

The purpose of this paper is to find out fixed point results for the family of multivalued mappings fulfilling a generalized rational type F-contractive conditions on a closed ball in complete dislocated b-metric space. An application to the system of integral equations is presented to show the novelty of our results. Our results extend several comparable results in the existing literature.

scholarly journals Fractional Integral Equations Tell Us How to Impose Initial Values in Fractional Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1093
Author(s):  
Daniel Cao Labora
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Initial Value ◽  
Major Question ◽  
Initial Values ◽  
Fractional Differential

One major question in Fractional Calculus is to better understand the role of the initial values in fractional differential equations. In this sense, there is no consensus about what is the reasonable fractional abstraction of the idea of “initial value problem”. This work provides an answer to this question. The techniques that are used involve known results concerning Volterra integral equations, and the spaces of summable fractional differentiability introduced by Samko et al. In a few words, we study the natural consequences in fractional differential equations of the already existing results involving existence and uniqueness for their integral analogues, in terms of the Riemann–Liouville fractional integral. In particular, we show that a fractional differential equation of a certain order with Riemann–Liouville derivatives demands, in principle, less initial values than the ceiling of the order to have a uniquely determined solution, in contrast to a widely extended opinion. We compute explicitly the amount of necessary initial values and the orders of differentiability where these conditions need to be imposed.

scholarly journals General fractional financial models of awareness with Caputo–Fabrizio derivative

2020 ◽  
Vol 12 (11) ◽  
pp. 168781402097552
Author(s):  
Amr MS Mahdy ◽  
Yasser Abd Elaziz Amer ◽  
Mohamed S Mohamed ◽  
Eslam Sobhy
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Numerical Simulations ◽  
Caputo Derivative ◽  
Existence And Uniqueness ◽  
Financial Models ◽  
Whole Number ◽  
Fractional System ◽  
Set Up ◽  
Theoretical Results

A Caputo–Fabrizio (CF) form a fractional-system mathematical model for the fractional financial models of awareness is suggested. The fundamental attributes of the model are explored. The existence and uniqueness of the suggest fractional financial models of awareness solutions are given through the fixed point hypothesis. The non-number request subordinate gives progressively adaptable and more profound data about the multifaceted nature of the elements of the proposed partial budgetary models of mindfulness model than the whole number request models set up previously. In order to confirm the theoretical results and numerical simulations studies with Caputo derivative are offered.

scholarly journals Relation Theoretic Common Fixed Point Results for Generalized Weak Nonlinear Contractions with an Application

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 49 ◽  
Author(s):  
Atiya Perveen ◽  
Idrees A. Khan ◽  
Mohammad Imdad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Integral Equations ◽  
Binary Relation ◽  
Metric Spaces ◽  
Partial Metric ◽  
System Of Integral Equations ◽  
Partial Metric Spaces ◽  
Nonlinear Contractions

In this paper, by introducing the concept of generalized Ćirić-type weak ( ϕ g , R ) -contraction, we prove some common fixed point results in partial metric spaces endowed with binary relation R . We also deduce some useful consequences showing the usability of our results. Finally, we present an application to establish the solution of a system of integral equations.

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