Solvability in weighted L1-spaces for the m-product of integral equations and model of the dynamics of the capillary rise

Metwali, Mohamed M. A.

doi:10.1016/j.jmaa.2022.126461

Cited by 3 publications

(1 citation statement)

References 19 publications

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“…e 3D time dispersion is carried out step by step according to the swamp integral method, and the local and global branches of the Roth model have serious consequences. By changing the integration step, the system exhibits complex dynamic behavior [2].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Systems of Differential Equations Based on Information Technology: Effects of Integral Step Size on Bifurcation and Chaos Control of Discrete Hindmarsh–Rose Models

Chen

2022

Mobile Information Systems

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Based on the differential equation dynamical system of information technology, this article analyzes how the integral step affects the bifurcation and chaos control of the discrete Hindmarsh–Rose model and its effect. By introducing the advantages of information technology in information management and information processing to the application of the differential equation dynamical system, the stability of the differential equation dynamical system model can be guaranteed. The integration step size is an important factor that affects the accuracy of the study results, and therefore, this paper understands how it affects the 3D discrete Hindmarsh–Rose model by choosing the appropriate step size.

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Section: Introductionmentioning

confidence: 99%

Dynamical Systems of Differential Equations Based on Information Technology: Effects of Integral Step Size on Bifurcation and Chaos Control of Discrete Hindmarsh–Rose Models

Chen

2022

Mobile Information Systems

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Discontinuous solutions of delay fractional integral equation via measures of noncompactness

Metwali

Alsallami

2023

MATH

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<abstract><p>This article considers the existence and the uniqueness of monotonic solutions of a delay functional integral equation of fractional order in the weighted Lebesgue space $ L_1^N({\mathbb{R}}^+) $. Our analysis uses a suitable measure of noncompactness, a modified version of Darbo's fixed point theorem, and fractional calculus in the mentioned space. An illustrated example to show the applicability and significance of our outcomes is included.</p></abstract>

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On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations

Alsaadi,

Kazemi,

Metwali

2023

MATH

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<abstract><p>Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.</p></abstract>

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Solvability in weighted L1-spaces for the m-product of integral equations and model of the dynamics of the capillary rise

Cited by 3 publications

References 19 publications

Dynamical Systems of Differential Equations Based on Information Technology: Effects of Integral Step Size on Bifurcation and Chaos Control of Discrete Hindmarsh–Rose Models

Dynamical Systems of Differential Equations Based on Information Technology: Effects of Integral Step Size on Bifurcation and Chaos Control of Discrete Hindmarsh–Rose Models

Discontinuous solutions of delay fractional integral equation via measures of noncompactness

On generalization of Petryshyn's fixed point theorem and its application to the product of $ n $-nonlinear integral equations

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