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dc.contributor.authorCuesta, Eduardo ( )
dc.contributor.authorPonce, Rodrigo ( )
dc.date.accessioned2022-03-09T19:47:58Z
dc.date.available2022-03-09T19:47:58Z
dc.date.issued2018-10-17
dc.identifier.citationCuesta, E., & Ponce, R. (2018). Well-posedness, regularity, and asymptotic behavior of continuous and discrete solutions of linear fractional integro-differential equations with time-dependent order. Electronic Journal of Differential Equations, 2018(173), pp. 1-27.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/15469
dc.description.abstractWe study the well-posedness of abstract time evolution fractional integro-differential equations of variable order u(t) = u0 + ∂-α(t) Au(t) + ƒ(t). Also we study the asymptotic behavior as t → +∞, and the regularity of solutions. Moreover, we present the asymptotic behavior of the discrete solution provided by a numerical method based on convolution quadratures, inherited from the behavior of the continuous solution. In this equation A plays the role of a linear operator of sectorial type. Several definitions proposed in the literature for the fractional integral of variable order are discussed, and the differences between the solutions provided for each of them are illustrated numerically. The definition we chose for this work is based on the Laplace transform, and we discuss the reasons for this choice.
dc.formatText
dc.format.extent27 pages
dc.format.medium1 file (.pdf)
dc.language.isoenen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectFractional integralsen_US
dc.subjectBanach spacesen_US
dc.subjectVariable orderen_US
dc.subjectConvolution quadraturesen_US
dc.titleWell-posedness, regularity, and asymptotic behavior of continuous and discrete solutions of linear fractional integro-differential equations with time-dependent orderen_US
dc.typepublishedVersion
txstate.documenttypeArticle
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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