Abstract

This talk is devoted to analyse different kinds of stabilities for higher order integro differential equations within appropriate metric spaces. We will consider the sigma-semi-Hyers-Ulam stability which is a new kind of stability somehow between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities. Sufficient conditions are obtained in view to guarantee Hyers-Ulam, sigma-semi-Hyers-Ulam and Hyers-Ulam-Rassias stabilities for such a class of integro-differential equations. We will be considering finite and infinite intervals as integration domains. Among the used techniques, we have fixed point argumentsand generalizations of the Bielecki metric.

Highlights

  • The study of properties associated with stability for functional, differential, integral and integro-differential has been widely diffused and has been a subject of great interest in the last seven decades earning particular interest due to their great number of applications in elasticity, semiconductors, heat conduction, fluid flow, scattering theory, chemical reactions and population dynamic, and others

  • We will consider the σ-semi-Hyers-Ulam stability which is a new kind of stability somehow between the Hyers-Ulam and the Hyers-Ulam-Rassias stabilities

  • Sufficient conditions are obtained in view to guarantee Hyers-Ulam, σ-semiHyers-Ulam and Hyers-Ulam-Rassias stabilities for such a class of integro-differential equations

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Summary

Stabilities for a class of higher order integrodifferential equations

Cite as: AIP Conference Proceedings 2046, 020012 (2018); https://doi.org/10.1063/1.5081532 Published Online: 04 December 2018 L. P. Castro, and A. M. Simões ARTICLES YOU MAY BE INTERESTED IN New convolutions for an oscillatory integral operator on the half-line AIP Conference Proceedings 2046, 020015 (2018); https://doi.org/10.1063/1.5081535 Convolutions and applications for the offset linear canonical transform via Hermite weights AIP Conference Proceedings 2046, 020014 (2018); https://doi.org/10.1063/1.5081534 On integral operators and equations generated by cosine and sine Fourier transforms AIP Conference Proceedings 2046, 020013 (2018); https://doi.org/10.1063/1.5081533

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