scholarly journals On Attractivity and Positivity of Solutions for Functional Integral Equations of Fractional Order

2013 ◽  
Vol 2013 ◽  
pp. 1-17
Author(s):  
Xianyong Huang ◽  
Junfei Cao
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Fractional Order ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Positivity Of Solutions ◽  
Unbounded Intervals ◽  
Functional Integral Equations

We investigate a class of functional integral equations of fractional order given byx(t)=q(t)+f1(t,x(α1(t)),x(α2(t)))+(f2(t,x(β1(t)),x(β2(t)))/Γ(α))×∫0t(t−s)α−1f3(t,s,x(γ1(s)),x(γ2(s)))ds: sufficient conditions for the existence, global attractivity, and ultimate positivity of solutions of the equations are derived. The main tools include the techniques of measures of noncompactness and a recent measure theoretic fixed point theorem of Dhage. Our investigations are placed in the Banach space of continuous and bounded real-valued functions defined on unbounded intervals. Moreover, two examples are given to illustrate our results.

scholarly journals Solvability of functional-integral equations (fractional order) using measure of noncompactness

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Reza Arab ◽  
Hemant Kumar Nashine ◽  
N. H. Can ◽  
Tran Thanh Binh
Keyword(s):  
Banach Space ◽  
Integral Equation ◽  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Arbitrary Measure ◽  
Functional Integral Equations

AbstractWe investigate the solutions of functional-integral equation of fractional order in the setting of a measure of noncompactness on real-valued bounded and continuous Banach space. We introduce a new μ-set contraction operator and derive generalized Darbo fixed point results using an arbitrary measure of noncompactness in Banach spaces. An illustration is given in support of the solution of a functional-integral equation of fractional order.

scholarly journals The Technique of Measures of Noncompactness in Banach Algebras and Its Applications to Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Józef Banaś ◽  
Szymon Dudek
Keyword(s):  
Banach Algebra ◽  
Integral Equations ◽  
Banach Algebras ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Half Axis ◽  
Functional Integral Equations

We study the solvability of some nonlinear functional integral equations in the Banach algebra of real functions defined, continuous, and bounded on the real half axis. We apply the technique of measures of noncompactness in order to obtain existence results for equations in question. Additionally, that technique allows us to obtain some characterization of considered integral equations. An example illustrating the obtained results is also included.

scholarly journals Solvability for generalized nonlinear two dimensional functional integral equations via measure of noncompactness

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Soniya Singh ◽  
Bhupander Singh ◽  
Kottakkaran Sooppy Nisar ◽  
Abd-Allah Hyder ◽  
M. Zakarya
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Existence Result ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Two Dimensional ◽  
Functional Integral Equations

AbstractIn this article, we provide the existence result for functional integral equations by using Petryshyn’s fixed point theorem connecting the measure of noncompactness in a Banach space. The results enlarge the corresponding results of several authors. We present fascinating examples of equations.

scholarly journals Global attractivity for Volterra type Hadamard fractional integral equations in Fréchet spaces

2018 ◽  
Vol 51 (1) ◽  
pp. 131-140
Author(s):  
Saïd Abbas ◽  
Ravi P. Agarwal ◽  
Mouffak Benchohra ◽  
Farida Berhoun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Fractional Integral ◽  
Global Attractivity ◽  
Functional Integral ◽  
Fréchet Spaces ◽  
Volterra Type ◽  
Functional Integral Equations ◽  
Hadamard Fractional Integral

Abstract In this paper, we present some results concerning the existence and the attractivity of solutions for some functional integral equations of Hadamard fractional order. We use an extension of the Burton-Kirk fixed point theorem in Fréchet spaces.

scholarly journals Weak Solutions of a Coupled System of Urysohn-Stieltjes Functional (Delayed) Integral Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
M. M. A. Al-Fadel
Keyword(s):  
Banach Space ◽  
Integral Equations ◽  
Weak Solutions ◽  
Reflexive Banach Space ◽  
Coupled System ◽  
Functional Integral ◽  
Existence Of Weak Solutions ◽  
Functional Integral Equations ◽  
Stieltjes Type

We study the existence of weak solutions for the coupled system of functional integral equations of Urysohn-Stieltjes type in the reflexive Banach spaceE. As an application, the coupled system of Hammerstien-Stieltjes functional integral equations is also studied.

scholarly journals Partially condensing mappings in partially ordered normed linar spaces and applications to functional integral equations

2014 ◽  
Vol 45 (4) ◽  
pp. 397-426 ◽  
Author(s):  
Bapurao Chandrabahan Dhage
Keyword(s):  
Integral Equations ◽  
Fixed Point Theorems ◽  
Normed Linear Space ◽  
Global Attractivity ◽  
Nonlinear Problems ◽  
Functional Integral ◽  
Nonlinear Functional ◽  
Partially Ordered ◽  
Monotonicity Conditions ◽  
Functional Integral Equations

In this paper, the author introduces a notion of partially condensing mappings in a partially ordered normed linear space and proves some hybrid fixed point theorems under certain mixed conditions of algebra, analysis and topology. The applications of abstract results presented here are given to some nonlinear functional integral equations for proving the existence as well as global attractivity of the comparable solutions under certain monotonicity conditions. The abstract theory presented here is very much useful to develop the algorithms for the solutions of some nonlinear problems of analysis and allied areas of mathematics. A realization of of our hypotheses is also indicated by a numerical example.

scholarly journals On existence theorems for some generalized nonlinear functional-integral equations with applications

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 2081-2091 ◽  
Author(s):  
Mishra Narayan ◽  
Mausumi Sen ◽  
Ram Mohapatra
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Banach Algebra ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Functional Integral ◽  
Measures Of Noncompactness ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In the present paper, utilizing the techniques of suitable measures of noncompactness in Banach algebra, we prove an existence theorem for nonlinear functional-integral equation which contains as particular cases several integral and functional-integral equations that appear in many branches of nonlinear analysis and its applications. We employ the fixed point theorems such as Darbo?s theorem in Banach algebra concerning the estimate on the solutions. We also provide a nontrivial example that explains the generalizations and applications of our main result.

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