Stability for generalized Caputo proportional fractional delay integro-differential equations
Abstract A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, expo...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-022-01595-0 |
| _version_ | 1818442637274775552 |
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| author | Martin Bohner Snezhana Hristova |
| author_facet | Martin Bohner Snezhana Hristova |
| author_sort | Martin Bohner |
| collection | DOAJ |
| description | Abstract A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included. |
| first_indexed | 2024-12-14T18:47:19Z |
| format | Article |
| id | doaj.art-8c3cbdc6fa8240dba87434bc27d8cb38 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-14T18:47:19Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-8c3cbdc6fa8240dba87434bc27d8cb382022-12-21T22:51:21ZengSpringerOpenBoundary Value Problems1687-27702022-03-012022111510.1186/s13661-022-01595-0Stability for generalized Caputo proportional fractional delay integro-differential equationsMartin Bohner0Snezhana Hristova1Missouri S&TFaculty of Mathematics and Informatics, University of Plovdiv “Paisii Hilendarski”Abstract A scalar nonlinear integro-differential equation with time-variable and bounded delays and generalized Caputo proportional fractional derivative is considered. The main goal of this paper is to study the stability properties of the zero solution. Results are given concerning stability, exponential stability, asymptotic stability, and boundedness of solutions. The investigations are based on an application of a quadratic Lyapunov function, its generalized Caputo proportional derivative, and a modification of the Razumikhin approach. Some auxiliary properties of the generalized Caputo proportional derivative are proved. Five illustrative examples are included.https://doi.org/10.1186/s13661-022-01595-0Generalized Caputo proportional fractional derivativeVariable delaysIntegro-differential fractional equationsInitial value problem |
| spellingShingle | Martin Bohner Snezhana Hristova Stability for generalized Caputo proportional fractional delay integro-differential equations Boundary Value Problems Generalized Caputo proportional fractional derivative Variable delays Integro-differential fractional equations Initial value problem |
| title | Stability for generalized Caputo proportional fractional delay integro-differential equations |
| title_full | Stability for generalized Caputo proportional fractional delay integro-differential equations |
| title_fullStr | Stability for generalized Caputo proportional fractional delay integro-differential equations |
| title_full_unstemmed | Stability for generalized Caputo proportional fractional delay integro-differential equations |
| title_short | Stability for generalized Caputo proportional fractional delay integro-differential equations |
| title_sort | stability for generalized caputo proportional fractional delay integro differential equations |
| topic | Generalized Caputo proportional fractional derivative Variable delays Integro-differential fractional equations Initial value problem |
| url | https://doi.org/10.1186/s13661-022-01595-0 |
| work_keys_str_mv | AT martinbohner stabilityforgeneralizedcaputoproportionalfractionaldelayintegrodifferentialequations AT snezhanahristova stabilityforgeneralizedcaputoproportionalfractionaldelayintegrodifferentialequations |