Existence the Solution of Coupled System of Quadratic Hybrid Functional Integral Equation in Banach Algebras

Karande, B. D.

doi:10.26782/jmcms.2020.09.00020

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…The technique has been used to establish the existence and approximation of various kinds of differential equations, such as neutral functional differential equations with delay and maxima, quadratic fractional integral equations with maxima, and hybrid functional differential equations. For more results, see [8,20,21].…”

Section: Introductionmentioning

confidence: 99%

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Benkhettou

Salim

Lazreg

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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In this paper, we study the following fractional differential equation involving the Atangana-Baleanu-Caputo fractional derivative: { A B C a D τ θ [ x ( ϑ ) − F ( ϑ , x ( ϑ ) ) ] = G ( ϑ , x ( ϑ ) ) , ϑ ∈ J : = [ a , b ] , x ( a ) = φ a ∈ ℝ . $$\left\{ {\matrix{ {AB{C_a}D_\tau ^\theta [x(\vartheta ) - F(\vartheta ,x(\vartheta ))] = G(\vartheta ,x(\vartheta )),\;\;\;{\kern 1pt} \vartheta \in J: = [a,b],} \hfill \cr {x(a) = {\varphi _a} \in .} \hfill \cr } } \right.$$ The result is based on a Dhage fixed point theorem. Further, an example is provided for the justification of our main result.

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Section: Introductionmentioning

confidence: 99%

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Benkhettou

Salim

Lazreg

et al. 2023

Annals of West University of Timisoara - Mathematics and Computer Science

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“…Recently, the existence results for fractional order quadratic functional integro-differential equation were studied and some attractivity results were obtained [23].…”

Section: Introductionmentioning

confidence: 99%

Qualitative Study for a Delay Quadratic Functional Integro-Differential Equation of Arbitrary (Fractional) Orders

2022

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Symmetry analysis has been applied to solve many differential equations, although determining the symmetries can be computationally intensive compared to other solution methods. In this work, we study some operators which keep the set of solutions invariant. We discuss the existence of solutions for two initial value problems of a delay quadratic functional integro-differential equation of arbitrary (fractional) orders and its corresponding integer orders equation. The existence of the maximal and the minimal solutions is proved. The sufficient condition for the uniqueness of the solutions is given. The continuous dependence of the unique solution on some data is studied. The continuation of the arbitrary (fractional) orders problem to the integer order problem is investigated.

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On existence theorems for coupled systems of quadratic Hammerstein-Urysohn integral equations in Orlicz spaces

Alsaadi

Metwali

2022

MATH

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<abstract><p>We present two existence theorems for a general system of functional quadratic Hammerstein-Urysohn integral equations in arbitrary Orlicz spaces $ L_\varphi $, namely when the generating $ N $-functions fulfill $ \Delta' $ and $ \Delta_3 $-conditions. The studied system contains many integral equations as special cases such as the Chandrasekhar equations, which have significant applications in technology and different disciplines of science. Our analysis is concerned with the fixed point approach and a measure of noncompactness.</p></abstract>

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Existence the Solution of Coupled System of Quadratic Hybrid Functional Integral Equation in Banach Algebras

Abstract: In this paper we prove the existence of solution of coupled system of quadratic hybrid functional integral equations. Our main result is based on the standard tools of fixed point theory. The Existence and locally attractivity is proved ℛ + .

Cited by 4 publications

References 22 publications

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Lakshmikantham Monotone Iterative Principle for Hybrid Atangana-Baleanu-Caputo Fractional Differential Equations

Qualitative Study for a Delay Quadratic Functional Integro-Differential Equation of Arbitrary (Fractional) Orders

On existence theorems for coupled systems of quadratic Hammerstein-Urysohn integral equations in Orlicz spaces

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