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 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 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 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.

scholarly journals Some New Generalization of Darbo’s Fixed Point Theorem and Its Application on Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 214 ◽  
Author(s):  
Anupam Das ◽  
Bipan Hazarika ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Control Function ◽  
Functional Integral ◽  
Existence Of A Solution ◽  
And Control ◽  
Functional Integral Equations

In this article, we propose some new fixed point theorem involving measure of noncompactness and control function. Further, we prove the existence of a solution of functional integral equations in two variables by using this fixed point theorem in Banach Algebra, and also illustrate the results with the help of an example.

scholarly journals On the solvability of a nonlinear functional integral equations via measure of noncompactness in

2020 ◽  
Vol 19 ◽  
pp. 74-88
Author(s):  
Wagdy G. El-Sayed ◽  
Mahmoud M. El-Borai ◽  
Mohamed M.A. Metwali ◽  
Nagwa I. Shemais
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Abstract Result ◽  
Nonlinear Functional ◽  
Darbo Fixed Point Theorem ◽  
Integrable Functions ◽  
Functional Integral Equations ◽  
Suitable Measure

Using the technique of a suitable measure of non-compactness and the Darbo fixed point theorem, we investigate the existence of a nonlinear functional integral equation of Urysohn type in the space of Lebesgue integrable functions Lp(RN). In this space, we show that our functional-integral equation has at least one solution. Finally, an example is also discussed to indicate the natural realizations of our abstract result.

scholarly journals On the solvability of some nonlinear functional integral equations on Lp(R+)

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1841-1850
Author(s):  
Mahmoud Bousselsal
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Functional Integral ◽  
Basic Tool ◽  
Nonlinear Functional ◽  
The Fixed Point Theorem ◽  
Functional Integral Equations

In this paper, we prove theorems on the existence of solutions in Lp(R+), 1 ? p < ?, for some functional integral equations. The basic tool used in the proof is the fixed point theorem due to Darbo with respect to so called measure of noncompactness. The obtained results generalize and extend several ones obtained earlier in many papers and monographs. An example which shows the applicability of our results is also included.

scholarly journals Application of measure of noncompactness for the system of functional integral equations

Filomat ◽  
2016 ◽  
Vol 30 (11) ◽  
pp. 3063-3073 ◽  
Author(s):  
Reza Arab
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Coupled Fixed Point ◽  
Functional Integral ◽  
System Of Integral Equations ◽  
Darbo Fixed Point Theorem ◽  
Functional Integral Equations

In this paper we introduce the notion of the generalized Darbo fixed point theorem and prove some fixed and coupled fixed point theorems in Banch space via the measure of non-compactness, which generalize the result of Aghajani et al.[6]. Our results generalize, extend, and unify several well-known comparable results in the literature. As an application, we study the existence of solutions for the system of integral equations.

scholarly journals Compactness Conditions in the Study of Functional, Differential, and Integral Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Józef Banaś ◽  
Kishin Sadarangani
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fixed Point Theorems ◽  
Functional Integral ◽  
Existence Results ◽  
Measures Of Noncompactness ◽  
Functional Differential ◽  
Functional Integral Equations ◽  
Differential And Integral Equations

We discuss some existence results for various types of functional, differential, and integral equations which can be obtained with the help of argumentations based on compactness conditions. We restrict ourselves to some classical compactness conditions appearing in fixed point theorems due to Schauder, Krasnosel’skii-Burton, and Schaefer. We present also the technique associated with measures of noncompactness and we illustrate its applicability in proving the solvability of some functional integral equations. Apart from this, we discuss the application of the mentioned technique to the theory of ordinary differential equations in Banach spaces.

The solvability of some nonlinear functional integral equations

2016 ◽  
Vol 53 (1) ◽  
pp. 7-21
Author(s):  
İsmet Özdemir ◽  
Ümit Çakan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Continuous Functions ◽  
Functional Integral ◽  
Space Of Continuous Functions ◽  
Nonlinear Functional ◽  
Functional Integral Equations

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of solutions of some nonlinear functional integral equations in the space of continuous functions on interval [0, a]. We give also some examples which show that the obtained results are applicable

Asymptotic stability of solutions for a class of nonlinear functional integral equations of fractional order

2016 ◽  
Vol 53 (2) ◽  
pp. 256-288
Author(s):  
Ümit Çakan ◽  
İsmet Özdemir
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Measure Of Noncompactness ◽  
Functional Integral ◽  
Asymptotically Stable ◽  
Stability Of Solutions ◽  
Nonlinear Functional ◽  
Bounded Functions ◽  
Stable Solutions ◽  
Functional Integral Equations

In this paper, using a Darbo type fixed point theorem associated with the measure of noncompactness we prove a theorem on the existence of asymptotically stable solutions of some nonlinear functional integral equations in the space of continuous and bounded functions on R+ = [0,∞). We also give some examples satisfying the conditions our existence theorem.

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