Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative

Abstract This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dyn...
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Autor*in:	Vishnukumar, K. S. [verfasserIn] Vellappandi, M. [verfasserIn] Govindaraj, V. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	Reachability (primary) Banach Fixed Point Theorem Iterative Technique Grammian Matrix

Anmerkung:	© Diogenes Co.Ltd 2024. 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: Fractional calculus and applied analysis - Springer International Publishing, 2004, 27(2024), 3 vom: 14. Feb., Seite 1328-1347
Übergeordnetes Werk:	volume:27 ; year:2024 ; number:3 ; day:14 ; month:02 ; pages:1328-1347

Links:	Volltext

DOI / URN:	10.1007/s13540-024-00245-9

Katalog-ID:	SPR05586970X

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520			\|a Abstract This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems.
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allfields	10.1007/s13540-024-00245-9 doi (DE-627)SPR05586970X (SPR)s13540-024-00245-9-e DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vishnukumar, K. S. verfasserin aut Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213 Vellappandi, M. verfasserin (orcid)0000-0003-2414-4415 aut Govindaraj, V. verfasserin aut Enthalten in Fractional calculus and applied analysis Springer International Publishing, 2004 27(2024), 3 vom: 14. Feb., Seite 1328-1347 Online-Ressource (DE-627)527574368 (DE-600)2276545-1 (DE-576)281336466 1314-2224 nnns volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347 https://dx.doi.org/10.1007/s13540-024-00245-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 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_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 31.00 Mathematik: Allgemeines VZ AR 27 2024 3 14 02 1328-1347
spelling	10.1007/s13540-024-00245-9 doi (DE-627)SPR05586970X (SPR)s13540-024-00245-9-e DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vishnukumar, K. S. verfasserin aut Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213 Vellappandi, M. verfasserin (orcid)0000-0003-2414-4415 aut Govindaraj, V. verfasserin aut Enthalten in Fractional calculus and applied analysis Springer International Publishing, 2004 27(2024), 3 vom: 14. Feb., Seite 1328-1347 Online-Ressource (DE-627)527574368 (DE-600)2276545-1 (DE-576)281336466 1314-2224 nnns volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347 https://dx.doi.org/10.1007/s13540-024-00245-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 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_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 31.00 Mathematik: Allgemeines VZ AR 27 2024 3 14 02 1328-1347
allfields_unstemmed	10.1007/s13540-024-00245-9 doi (DE-627)SPR05586970X (SPR)s13540-024-00245-9-e DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vishnukumar, K. S. verfasserin aut Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213 Vellappandi, M. verfasserin (orcid)0000-0003-2414-4415 aut Govindaraj, V. verfasserin aut Enthalten in Fractional calculus and applied analysis Springer International Publishing, 2004 27(2024), 3 vom: 14. Feb., Seite 1328-1347 Online-Ressource (DE-627)527574368 (DE-600)2276545-1 (DE-576)281336466 1314-2224 nnns volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347 https://dx.doi.org/10.1007/s13540-024-00245-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 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_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 31.00 Mathematik: Allgemeines VZ AR 27 2024 3 14 02 1328-1347
allfieldsGer	10.1007/s13540-024-00245-9 doi (DE-627)SPR05586970X (SPR)s13540-024-00245-9-e DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vishnukumar, K. S. verfasserin aut Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213 Vellappandi, M. verfasserin (orcid)0000-0003-2414-4415 aut Govindaraj, V. verfasserin aut Enthalten in Fractional calculus and applied analysis Springer International Publishing, 2004 27(2024), 3 vom: 14. Feb., Seite 1328-1347 Online-Ressource (DE-627)527574368 (DE-600)2276545-1 (DE-576)281336466 1314-2224 nnns volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347 https://dx.doi.org/10.1007/s13540-024-00245-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 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_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 31.00 Mathematik: Allgemeines VZ AR 27 2024 3 14 02 1328-1347
allfieldsSound	10.1007/s13540-024-00245-9 doi (DE-627)SPR05586970X (SPR)s13540-024-00245-9-e DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn 31.00 bkl Vishnukumar, K. S. verfasserin aut Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213 Vellappandi, M. verfasserin (orcid)0000-0003-2414-4415 aut Govindaraj, V. verfasserin aut Enthalten in Fractional calculus and applied analysis Springer International Publishing, 2004 27(2024), 3 vom: 14. Feb., Seite 1328-1347 Online-Ressource (DE-627)527574368 (DE-600)2276545-1 (DE-576)281336466 1314-2224 nnns volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347 https://dx.doi.org/10.1007/s13540-024-00245-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_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_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 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_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 31.00 Mathematik: Allgemeines VZ AR 27 2024 3 14 02 1328-1347
language	English
source	Enthalten in Fractional calculus and applied analysis 27(2024), 3 vom: 14. Feb., Seite 1328-1347 volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347
sourceStr	Enthalten in Fractional calculus and applied analysis 27(2024), 3 vom: 14. Feb., Seite 1328-1347 volume:27 year:2024 number:3 day:14 month:02 pages:1328-1347
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bklname	Mathematik: Allgemeines
institution	findex.gbv.de
topic_facet	Reachability (primary) Banach Fixed Point Theorem Iterative Technique Grammian Matrix
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container_title	Fractional calculus and applied analysis
authorswithroles_txt_mv	Vishnukumar, K. S. @@aut@@ Vellappandi, M. @@aut@@ Govindaraj, V. @@aut@@
publishDateDaySort_date	2024-02-14T00:00:00Z
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author	Vishnukumar, K. S.
spellingShingle	Vishnukumar, K. S. ddc 510 ssgn 17,1 bkl 31.00 misc Reachability (primary) misc Banach Fixed Point Theorem misc Iterative Technique misc Grammian Matrix Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
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topic_title	510 VZ 17,1 ssgn 31.00 bkl Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative Reachability (primary) (dpeaa)DE-He213 Banach Fixed Point Theorem (dpeaa)DE-He213 Iterative Technique (dpeaa)DE-He213 Grammian Matrix (dpeaa)DE-He213
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title	Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
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title_full	Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
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title_sort	reachability of time-varying fractional dynamical systems with riemann-liouville fractional derivative
title_auth	Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
abstract	Abstract This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. © Diogenes Co.Ltd 2024. 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 This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition matrix is used to solve the time-varying systems. Using the reachability Grammian matrix, the reachability linear time-varying fractional dynamical system is discussed. The existence and uniqueness of a solution of a nonlinear time-varying fractional dynamical system is established, and sufficient conditions for the reachability of nonlinear time-varying fractional dynamical systems are obtained with the help of Banach fixed point theorem. The reachability results are proved for a time-varying integro-fractional dynamical system for a particular case. A successive approximation method is proposed to give numerical solutions to the reachability problems. © Diogenes Co.Ltd 2024. 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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title_short	Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
url	https://dx.doi.org/10.1007/s13540-024-00245-9
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author2	Vellappandi, M. Govindaraj, V.
author2Str	Vellappandi, M. Govindaraj, V.
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doi_str	10.1007/s13540-024-00245-9
up_date	2024-07-03T18:35:10.844Z
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative

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