Cuesta, EduardoPonce, Rodrigo2022-03-092022-03-092018-10-17Cuesta, 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. <i>Electronic Journal of Differential Equations, 2018</i>(173), pp. 1-27.1072-6691https://hdl.handle.net/10877/15469We 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.Text27 pages1 file (.pdf)enAttribution 4.0 InternationalFractional integralsBanach spacesVariable orderConvolution quadraturesArticle