Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays

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dc.contributor.authorHristova, Snezhana
dc.contributor.authorTunc, Cemil
dc.date.accessioned2021-10-25T21:09:30Z
dc.date.available2021-10-25T21:09:30Z
dc.date.issued2019-02-19
dc.description.abstractWe use Lyapunov functions to study stability of the first-order Volterra integro-differential equation with Caputo fractional derivative Ct0Dqtx(t) = -α(t)ƒ(x(t)) + ∫tt-r B(t, s)g(s, x(s))ds + h(t, x(t), x(t - τ(t))). For the Lyapunov functions, we consider three types of fractional derivatives. By means of these derivatives, we obtain new sufficient conditions for stability and uniformly stability of solutions. We consider both constant and time variable bounded delays, and illustrated our results with an example.
dc.description.departmentMathematics
dc.formatText
dc.format.extent11 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHristova, S., & Tunç, C. (2019). Stability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays. <i>Electronic Journal of Differential Equations, 2019</i>(30), pp. 1-11.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14728
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, 2019, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectfractional derivative
dc.subjectintegro-differential equation
dc.subjectdelay
dc.subjectLyapunov functional
dc.subjectstability
dc.titleStability of nonlinear Volterra integro-differential equations with Caputo fractional derivative and bounded delays
dc.typeArticle

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