Exponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations

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dc.contributor.authorBrestovanska, Eva
dc.contributor.authorMedved, Milan
dc.date.accessioned2022-09-08T14:40:32Z
dc.date.available2022-09-08T14:40:32Z
dc.date.issued2017-11-10
dc.description.abstractThe main aim of this paper is to prove a theorem on the exponential stability of the zero solution of a class of integro-differential equations, whose right-hand sides involve the Riemann-Liouville fractional integrals of different orders and we assume that they are polynomially bounded. Equations of that type can be obtained e.g. from fractionally damped pendulum equations, where the fractional damping terms depend on the Caputo fractional derivatives of solutions. The set of initial values of solutions that converge to the origin is also determined. We also prove an existence and uniqueness theorem for this type of equations, which we use in the proof of the stability theorem.
dc.description.departmentMathematics
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationBrestovanska, E., & Medved, M. (2017). Exponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations. <i>Electronic Journal of Differential Equations, 2017</i>(280), pp. 1-17.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/16125
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2017, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectRiemann-Liouville integral
dc.subjectRiemann-Liouville derivative
dc.subjectCaputo derivative
dc.subjectFractional differential equation
dc.subjectExponential stability
dc.titleExponential stability of solutions of nonlinear fractionally perturbed ordinary differential equations
dc.typeArticle

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