On the perturbation of Volterra integro-differential equations

Jung, Soon-Mo; Şevgin, Sebaheddin; Şevli, Hamdullah

doi:10.1016/j.aml.2012.10.018

Cited by 7 publications

(3 citation statements)

References 9 publications

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“…Recently in [11] the authors jointly with S.-M. Jung proved that if p : I → R, q : I → R, K : I × I → R and ϕ : I → [0, ∞) are sufficiently smooth functions and if a continuously differentiable function u : I → R satisfies the perturbed Volterra integro-differential equation…”

Section: Introductionmentioning

confidence: 99%

Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

Şevgin¹,

Şevli²

2016

J. Nonlinear Sci. Appl.

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Section: Introductionmentioning

confidence: 99%

Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

Şevgin¹,

Şevli²

2016

J. Nonlinear Sci. Appl.

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“…It bears the name Vito Volterra after the Italian mathematician who conducted substantial research on integral equations and their characteristics. The authors in [4]…”

Section: Introductionmentioning

confidence: 99%

Stability Analysis of First Order Integro-Differential Equations With the Successive Approximation Method

Jargess Abdul Wahid Abdulla

2023

anvi

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The Ulam stability theory provides a framework to provide the stability of functional equations, including integrodifferential equations. This manuscript focuses on the Ulam-stability analysis of the first-order integrodifferential equation. First-order integrodifferential equations combine differential and integral terms, making their analysis challenging and intriguing. The Ulam-stability concept investigates the behaviour of solutions under perturbations in the equation's inputs or initial conditions. It offers valuable insights into the long-term behaviour and robustness of the solutions in the presence of minor disturbances. The results obtained in this study contribute to the understanding of stability properties of first-order integrodifferential equations and provide a foundation for further research in this area. The Ulam stability analysis offers valuable insights into the behaviour of these equations, aiding in their application to diverse domains, including physics, engineering, and mathematical modeling.

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“…The concept of stability for functional, differential, integral and integro-differential equations has been studied in a quite extensive way during the last six decades and have earned particular interest due to their great number of applications (see [1,3,5,6,8,9,10,11,12,13,14,15,16,18,19,20,21,22,23,26] and the references therein). This occurs with particular emphasis in the case of Hyers-Ulam and Hyers-Ulam-Rassias stabilities.…”

Section: Introductionmentioning

confidence: 99%

Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

Castro

Simões

2018

Nonlinear Systems and Complexity

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On the perturbation of Volterra integro-differential equations

Cited by 7 publications

References 9 publications

Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

Stability of a nonlinear Volterra integro-differential equation via a fixed point approach

Stability Analysis of First Order Integro-Differential Equations With the Successive Approximation Method

Hyers-Ulam and Hyers-Ulam-Rassias Stability for a Class of Integro-Differential Equations

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