Caputo–Hadamard fractional differential equations on time scales: Numerical scheme, asymptotic stability, and chaos
This study investigates Caputo–Hadamard fractional differential equations on time scales. The Hadamard fractional sum and difference are defined for the first time. A general logarithm function on time scales is used as a kernel function. New fractional difference equations and their equivalent frac...
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Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2022-09, Vol.32 (9), p.093143-093143 |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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Zusammenfassung: | This study investigates Caputo–Hadamard fractional differential equations on time scales. The Hadamard fractional sum and difference are defined for the first time. A general logarithm function on time scales is used as a kernel function. New fractional difference equations and their equivalent fractional sum equations are presented by the use of fundamental theorems. Gronwall inequality, asymptotical stability conditions, and two discrete-time Mittag–Leffler functions of Hadamard type are obtained. Numerical schemes are provided and chaos in fractional discrete-time logistic equation and neural network equations are reported. |
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ISSN: | 1054-1500 1089-7682 |
DOI: | 10.1063/5.0098375 |