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
Hauptverfasser: Wu, Guo-Cheng, Song, Ting-Ting, Wang, Shuqiang
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Sprache:eng
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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.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0098375