A New Look at the Initial Condition Problem
In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generalit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1771 |
| _version_ | 1797498029871202304 |
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| author | Manuel D. Ortigueira |
| author_facet | Manuel D. Ortigueira |
| author_sort | Manuel D. Ortigueira |
| collection | DOAJ |
| description | In this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems. |
| first_indexed | 2024-03-10T03:28:37Z |
| format | Article |
| id | doaj.art-0caf4987ef7744c3b72e362c990e94a5 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:28:37Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-0caf4987ef7744c3b72e362c990e94a52023-11-23T12:02:12ZengMDPI AGMathematics2227-73902022-05-011010177110.3390/math10101771A New Look at the Initial Condition ProblemManuel D. Ortigueira0Centre of Technology and Systems—UNINOVA and Department of Electrical Engineering, NOVA School of Science and Technology of NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, PortugalIn this paper, some myths associated to the initial condition problem are studied and demystified. It is shown that the initial conditions provided by the one-sided Laplace transform are not those required for Riemann-Liouville and Caputo derivatives. The problem is studied and solved with generality as well as applied to continuous-time fractional autoregressive-moving average systems.https://www.mdpi.com/2227-7390/10/10/1771initial conditionsfractional derivativelinear systemsRiemann-Liouville derivativeCaputo derivativeFARMA |
| spellingShingle | Manuel D. Ortigueira A New Look at the Initial Condition Problem Mathematics initial conditions fractional derivative linear systems Riemann-Liouville derivative Caputo derivative FARMA |
| title | A New Look at the Initial Condition Problem |
| title_full | A New Look at the Initial Condition Problem |
| title_fullStr | A New Look at the Initial Condition Problem |
| title_full_unstemmed | A New Look at the Initial Condition Problem |
| title_short | A New Look at the Initial Condition Problem |
| title_sort | new look at the initial condition problem |
| topic | initial conditions fractional derivative linear systems Riemann-Liouville derivative Caputo derivative FARMA |
| url | https://www.mdpi.com/2227-7390/10/10/1771 |
| work_keys_str_mv | AT manueldortigueira anewlookattheinitialconditionproblem AT manueldortigueira newlookattheinitialconditionproblem |