scholarly journals Existence solution of a system of differential equations using generalized Darbo's fixed point theorem

2021 ◽  
Vol 6 (12) ◽  
pp. 13358-13369
Author(s):  
Rahul ◽  
◽  
Nihar Kumar Mahato
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solution ◽  
System Of Differential Equations ◽  
Darbo’S Fixed Point Theorem ◽  
Darbo Fixed Point Theorem

<abstract><p>In this paper, we proposed a generalized of Darbo's fixed point theorem via the concept of operators $ S(\bullet; .) $ associated with the measure of noncompactness. Using this generalized Darbo fixed point theorem, we have given the existence of solution of a system of differential equations. At the end, we have given an example which supports our findings.</p></abstract>

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

MEASURES OF NONCOMPACTNESS IN A SOBOLEV SPACE AND INTEGRO-DIFFERENTIAL EQUATIONS

2016 ◽  
Vol 94 (3) ◽  
pp. 497-506
Author(s):  
REZA ALLAHYARI ◽  
REZA ARAB ◽  
ALI SHOLE HAGHIGHI
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Sobolev Space ◽  
Differential Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Measures Of Noncompactness ◽  
Darbo’S Fixed Point Theorem

The aim of this paper is to introduce a new measure of noncompactness on the Sobolev space$W^{n,p}[0,T]$. As an application, we investigate the existence of solutions for some classes of functional integro-differential equations in this space using Darbo’s fixed point theorem.

scholarly journals An extension of Darbo’s fixed point theorem for a class of system of nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Amar Deep ◽  
Deepmala ◽  
Jamal Rezaei Roshan ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Results ◽  
Nonlinear Integral Equations ◽  
Existence Of A Solution ◽  
Darbo’S Fixed Point Theorem ◽  
Novi Sad

Abstract We introduce an extension of Darbo’s fixed point theorem via a measure of noncompactness in a Banach space. By using our extension we study the existence of a solution for a system of nonlinear integral equations, which is an extended result of (Aghajani and Haghighi in Novi Sad J. Math. 44(1):59–73, 2014). We give an example to show the specified existence results.

scholarly journals Application of a fixed point theorem on infinite cartesian product to an infinite system of differential equations

2021 ◽  
Vol 37 (2) ◽  
pp. 259-263
Author(s):  
MARCEL-ADRIAN ŞERBAN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Infinite System ◽  
Cartesian Product ◽  
System Of Differential Equations ◽  
Abstract Result ◽  
Infinite Dimensional ◽  
Contraction Theorem

"In the paper Operators on infinite dimensional cartesian product, (Analele Univ. Vest Timişoara, Mat. Inform., 48 (2010), 253–263), by I. A. Rus and M. A. Şerban, the authors give a generalization of the Fibre contraction theorem on infinite dimensional cartesian product. In this paper we give an application of this abstract result to an infinite system of differential equations. "

scholarly journals Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 492
Author(s):  
Babak Mohammadi ◽  
Ali Asghar Shole Haghighi ◽  
Maryam Khorshidi ◽  
Manuel De la Sen ◽  
Vahid Parvaneh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Main Tool ◽  
System Of Integral Equations ◽  
Darbo’S Fixed Point Theorem

In this paper, an extension of Darbo’s fixed point theorem via θ -F-contractions in a Banach space has been presented. Measure of noncompactness approach is the main tool in the presentation of our proofs. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

scholarly journals ON THE CONTROLLABILITY OF IMPULSIVE FUNCTIONAL INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES

2019 ◽  
Vol 6 (1) ◽  
pp. 17-22
Author(s):  
Valliammal N ◽  
Ravichandran C
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Banach Spaces ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Mönch Fixed Point Theorem

In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.

scholarly journals Caputo-Fabrizio fractional differential equations in Frechet spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 373-386
Author(s):  
Said Abbas ◽  
Mouffak Benchohra ◽  
Hafsa Gorine
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Measure Of Noncompactness ◽  
Fréchet Spaces ◽  
Uniqueness Of Solutions ◽  
Darbo Fixed Point Theorem ◽  
Fractional Differential

This paper deals with some existence and uniqueness of solutions for a class of functional Caputo-Fabrizio fractional differential equations. Some applications are made of a generalization of the classical Darbo fixed point theorem for Frechet spaces associate with the concept of measure of noncompactness. The last section illustrates our results with some examples.

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