dc.contributor.author Cuesta, Eduardo ( ) dc.contributor.author Ponce, Rodrigo ( ) dc.date.accessioned 2022-03-09T19:47:58Z dc.date.available 2022-03-09T19:47:58Z dc.date.issued 2018-10-17 dc.identifier.citation Cuesta, 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.issn 1072-6691 dc.identifier.uri https://digital.library.txstate.edu/handle/10877/15469 dc.description.abstract We 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.format Text dc.format.extent 27 pages dc.format.medium 1 file (.pdf) dc.language.iso en en_US dc.publisher Texas State University, Department of Mathematics en_US dc.source Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. dc.subject Fractional integrals en_US dc.subject Banach spaces en_US dc.subject Variable order en_US dc.subject Convolution quadratures en_US dc.title Well-posedness, regularity, and asymptotic behavior of continuous and discrete solutions of linear fractional integro-differential equations with time-dependent order en_US dc.type publishedVersion txstate.documenttype Article dc.rights.license This work is licensed under a Creative Commons Attribution 4.0 International License.
﻿