Singular regularization of operator equations in L1 spaces via fractional differential equations
| dc.contributor.author | Karakostas, George L. | |
| dc.contributor.author | Purnaras, Ioannis K. | |
| dc.date.accessioned | 2023-05-25T12:54:19Z | |
| dc.date.available | 2023-05-25T12:54:19Z | |
| dc.date.issued | 2016-01-04 | |
| dc.description.abstract | An abstract causal operator equation y=Ay defined on a space of the form L1([0,τ],X), with X a Banach space, is regularized by the fractional differential equation ε(Dα0yε)(t) = -yε(t) + (Ayε)(t), t ∈ [0,τ], where Dα0 denotes the (left) Riemann-Liouville derivative of order α ∈ (0,1). The main procedure lies on properties of the Mittag-Leffler function combined with some facts from convolution theory. Our results complete relative ones that have appeared in the literature; see, e.g. [5] in which regularization via ordinary differential equations is used. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 15 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Karakostas, G. L., & Purnaras, I. K. (2016). Singular regularization of operator equations in L1 spaces via fractional differential equations. <i>Electronic Journal of Differential Equations, 2016</i>(01), pp. 1-15. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/16873 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2016, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Causal operator equations | |
| dc.subject | Fractional differential equations | |
| dc.subject | Regularization | |
| dc.subject | Banach space | |
| dc.title | Singular regularization of operator equations in L1 spaces via fractional differential equations | |
| dc.type | Article |