Invariant set theorems for non-autonomous time-fractional systems

Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new...
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Autor*in:	Lahrouz, Aadil [verfasserIn] Hajjami, Riane [verfasserIn] El Jarroudi, Mustapha [verfasserIn] Settati, Adel [verfasserIn] Erriani, Mustapha [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Fractional systems Invariant set theorem Asymptotic stability Uniform asymptotic stability

Anmerkung:	© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Übergeordnetes Werk:	Enthalten in: International journal of dynamics and control - Springer Berlin Heidelberg, 2013, 12(2023), 7 vom: 31. Dez., Seite 2280-2294
Übergeordnetes Werk:	volume:12 ; year:2023 ; number:7 ; day:31 ; month:12 ; pages:2280-2294

Links:	Volltext

DOI / URN:	10.1007/s40435-023-01361-9

Katalog-ID:	SPR05646472X

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520			\|a Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results.
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700	1		\|a Erriani, Mustapha \|e verfasserin \|4 aut
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allfields	10.1007/s40435-023-01361-9 doi (DE-627)SPR05646472X (SPR)s40435-023-01361-9-e DE-627 ger DE-627 rakwb eng 510 VZ Lahrouz, Aadil verfasserin (orcid)0000-0002-6050-6586 aut Invariant set theorems for non-autonomous time-fractional systems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213 Hajjami, Riane verfasserin aut El Jarroudi, Mustapha verfasserin aut Settati, Adel verfasserin aut Erriani, Mustapha verfasserin aut Enthalten in International journal of dynamics and control Springer Berlin Heidelberg, 2013 12(2023), 7 vom: 31. Dez., Seite 2280-2294 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294 https://dx.doi.org/10.1007/s40435-023-01361-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2023 7 31 12 2280-2294
spelling	10.1007/s40435-023-01361-9 doi (DE-627)SPR05646472X (SPR)s40435-023-01361-9-e DE-627 ger DE-627 rakwb eng 510 VZ Lahrouz, Aadil verfasserin (orcid)0000-0002-6050-6586 aut Invariant set theorems for non-autonomous time-fractional systems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213 Hajjami, Riane verfasserin aut El Jarroudi, Mustapha verfasserin aut Settati, Adel verfasserin aut Erriani, Mustapha verfasserin aut Enthalten in International journal of dynamics and control Springer Berlin Heidelberg, 2013 12(2023), 7 vom: 31. Dez., Seite 2280-2294 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294 https://dx.doi.org/10.1007/s40435-023-01361-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2023 7 31 12 2280-2294
allfields_unstemmed	10.1007/s40435-023-01361-9 doi (DE-627)SPR05646472X (SPR)s40435-023-01361-9-e DE-627 ger DE-627 rakwb eng 510 VZ Lahrouz, Aadil verfasserin (orcid)0000-0002-6050-6586 aut Invariant set theorems for non-autonomous time-fractional systems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213 Hajjami, Riane verfasserin aut El Jarroudi, Mustapha verfasserin aut Settati, Adel verfasserin aut Erriani, Mustapha verfasserin aut Enthalten in International journal of dynamics and control Springer Berlin Heidelberg, 2013 12(2023), 7 vom: 31. Dez., Seite 2280-2294 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294 https://dx.doi.org/10.1007/s40435-023-01361-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2023 7 31 12 2280-2294
allfieldsGer	10.1007/s40435-023-01361-9 doi (DE-627)SPR05646472X (SPR)s40435-023-01361-9-e DE-627 ger DE-627 rakwb eng 510 VZ Lahrouz, Aadil verfasserin (orcid)0000-0002-6050-6586 aut Invariant set theorems for non-autonomous time-fractional systems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213 Hajjami, Riane verfasserin aut El Jarroudi, Mustapha verfasserin aut Settati, Adel verfasserin aut Erriani, Mustapha verfasserin aut Enthalten in International journal of dynamics and control Springer Berlin Heidelberg, 2013 12(2023), 7 vom: 31. Dez., Seite 2280-2294 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294 https://dx.doi.org/10.1007/s40435-023-01361-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2023 7 31 12 2280-2294
allfieldsSound	10.1007/s40435-023-01361-9 doi (DE-627)SPR05646472X (SPR)s40435-023-01361-9-e DE-627 ger DE-627 rakwb eng 510 VZ Lahrouz, Aadil verfasserin (orcid)0000-0002-6050-6586 aut Invariant set theorems for non-autonomous time-fractional systems 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213 Hajjami, Riane verfasserin aut El Jarroudi, Mustapha verfasserin aut Settati, Adel verfasserin aut Erriani, Mustapha verfasserin aut Enthalten in International journal of dynamics and control Springer Berlin Heidelberg, 2013 12(2023), 7 vom: 31. Dez., Seite 2280-2294 (DE-627)745617794 (DE-600)2714518-9 2195-2698 nnns volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294 https://dx.doi.org/10.1007/s40435-023-01361-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 12 2023 7 31 12 2280-2294
language	English
source	Enthalten in International journal of dynamics and control 12(2023), 7 vom: 31. Dez., Seite 2280-2294 volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294
sourceStr	Enthalten in International journal of dynamics and control 12(2023), 7 vom: 31. Dez., Seite 2280-2294 volume:12 year:2023 number:7 day:31 month:12 pages:2280-2294
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Fractional systems Invariant set theorem Asymptotic stability Uniform asymptotic stability
dewey-raw	510
isfreeaccess_bool	false
container_title	International journal of dynamics and control
authorswithroles_txt_mv	Lahrouz, Aadil @@aut@@ Hajjami, Riane @@aut@@ El Jarroudi, Mustapha @@aut@@ Settati, Adel @@aut@@ Erriani, Mustapha @@aut@@
publishDateDaySort_date	2023-12-31T00:00:00Z
hierarchy_top_id	745617794
dewey-sort	3510
id	SPR05646472X
language_de	englisch
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author	Lahrouz, Aadil
spellingShingle	Lahrouz, Aadil ddc 510 misc Fractional systems misc Invariant set theorem misc Asymptotic stability misc Uniform asymptotic stability Invariant set theorems for non-autonomous time-fractional systems
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topic_title	510 VZ Invariant set theorems for non-autonomous time-fractional systems Fractional systems (dpeaa)DE-He213 Invariant set theorem (dpeaa)DE-He213 Asymptotic stability (dpeaa)DE-He213 Uniform asymptotic stability (dpeaa)DE-He213
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title	Invariant set theorems for non-autonomous time-fractional systems
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title_sort	invariant set theorems for non-autonomous time-fractional systems
title_auth	Invariant set theorems for non-autonomous time-fractional systems
abstract	Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstractGer	Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
abstract_unstemmed	Abstract Though the commonly used fractional Lyapunov stability and LaSalle theorems have been beneficial in the development of the theory and applications of fractional derivatives, their proofs hold certain flaws which can make their applicability questionable. From this point, we established new invariant set-based stability theorems for fractional order Caputo systems. As a consequence, we have obtained the fractional version of the Lyapunov stability theorem. In addition, sufficient conditions for the uniform asymptotic stability of Caputo systems are derived. Finally, two illustrative applications from population dynamics are presented to validate the effectiveness of the theoretical results. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
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container_issue	7
title_short	Invariant set theorems for non-autonomous time-fractional systems
url	https://dx.doi.org/10.1007/s40435-023-01361-9
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author2	Hajjami, Riane El Jarroudi, Mustapha Settati, Adel Erriani, Mustapha
author2Str	Hajjami, Riane El Jarroudi, Mustapha Settati, Adel Erriani, Mustapha
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doi_str	10.1007/s40435-023-01361-9
up_date	2024-07-10T07:10:31.636Z
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Invariant set theorems for non-autonomous time-fractional systems

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