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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Continuability of Lienard's Type System with Generalized Local Derivative

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 1--11 | DOI:10.5890/DNC.2023.03.001

George E. Chatzarakis, Juan E. N\'{a}poles Vald\'{e}s

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Abstract

In this paper, we study the boundedness and continuability of the solutions of a generalized Li\'{e}nard type system, using fractional derivatives of the local type. We obtain sufficient conditions for the solutions to be bounded and continuous by a suitably defined Lyapunov function. We illustrate the results and suggest extensions to asymptotic stability, through various examples adapted from the relevant literature.

Acknowledgments

The authors thank the Reviewer for his/her constructive suggestions and useful corrections that improved the content of the paper.

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