Stability of mild solutions of the fractional nonlinear abstract Cauchy problem
Since the first work on Ulam-Hyers stabilities of differential equation solutions to date, many important and relevant papers have been published, both in the sense of integer order and fractional order differential equations. However, when we enter the field of fractional calculus, in particular, i...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2022015?viewType=HTML |
| _version_ | 1828103867771912192 |
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| author | J. Vanterler da C. Sousa Kishor D. Kucche E. Capelas de Oliveira |
| author_facet | J. Vanterler da C. Sousa Kishor D. Kucche E. Capelas de Oliveira |
| author_sort | J. Vanterler da C. Sousa |
| collection | DOAJ |
| description | Since the first work on Ulam-Hyers stabilities of differential equation solutions to date, many important and relevant papers have been published, both in the sense of integer order and fractional order differential equations. However, when we enter the field of fractional calculus, in particular, involving fractional differential equations, the path that is still long to be traveled, although there is a range of published works. In this sense, in this paper, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of mild solutions for fractional nonlinear abstract Cauchy problem in the intervals [0,T] and [0,∞) using Banach fixed point theorem. |
| first_indexed | 2024-04-11T09:32:21Z |
| format | Article |
| id | doaj.art-7f9001c8296747c8b5db9e66ed134694 |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-11T09:32:21Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-7f9001c8296747c8b5db9e66ed1346942022-12-22T04:31:50ZengAIMS PressElectronic Research Archive2688-15942022-01-0130127228810.3934/era.2022015Stability of mild solutions of the fractional nonlinear abstract Cauchy problemJ. Vanterler da C. Sousa0Kishor D. Kucche1E. Capelas de Oliveira21. Department of Applied Mathematics, State University of Campinas, Imecc, 13083-859, Campinas, SP, Brazil2. Department of Mathematics, Shivaji University, Kolhapur, Maharashtra 416 004, India1. Department of Applied Mathematics, State University of Campinas, Imecc, 13083-859, Campinas, SP, BrazilSince the first work on Ulam-Hyers stabilities of differential equation solutions to date, many important and relevant papers have been published, both in the sense of integer order and fractional order differential equations. However, when we enter the field of fractional calculus, in particular, involving fractional differential equations, the path that is still long to be traveled, although there is a range of published works. In this sense, in this paper, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of mild solutions for fractional nonlinear abstract Cauchy problem in the intervals [0,T] and [0,∞) using Banach fixed point theorem.https://www.aimspress.com/article/doi/10.3934/era.2022015?viewType=HTMLfractional nonlinear abstract cauchyulam-hyers stabilitiessemigroup theorymild solutionbanach fixed point theorem |
| spellingShingle | J. Vanterler da C. Sousa Kishor D. Kucche E. Capelas de Oliveira Stability of mild solutions of the fractional nonlinear abstract Cauchy problem Electronic Research Archive fractional nonlinear abstract cauchy ulam-hyers stabilities semigroup theory mild solution banach fixed point theorem |
| title | Stability of mild solutions of the fractional nonlinear abstract Cauchy problem |
| title_full | Stability of mild solutions of the fractional nonlinear abstract Cauchy problem |
| title_fullStr | Stability of mild solutions of the fractional nonlinear abstract Cauchy problem |
| title_full_unstemmed | Stability of mild solutions of the fractional nonlinear abstract Cauchy problem |
| title_short | Stability of mild solutions of the fractional nonlinear abstract Cauchy problem |
| title_sort | stability of mild solutions of the fractional nonlinear abstract cauchy problem |
| topic | fractional nonlinear abstract cauchy ulam-hyers stabilities semigroup theory mild solution banach fixed point theorem |
| url | https://www.aimspress.com/article/doi/10.3934/era.2022015?viewType=HTML |
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