Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 30, Issue 7, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X22501456
Keywords
Hadarnard Fractional Derivative; Discrete Fractional Calculus; Time Scales
Funding
- National Natural Science Foundation of China (NSFC) [62076141]
- Sichuan Youth Science and Technology Foundation [2022JDJQ0046]
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This study introduces a Hadamard fractional sum based on the time-scale theory and defines h-fractional difference. It proves fundamental theorems and presents initial value problems of fractional difference equations, providing their equivalent fractional sum equations. It also derives the discrete Mittag-Leffler function solutions for linear fractional difference equations. The study concludes that the new discrete fractional calculus of Hadamard type is well defined.
This study defines a Hadamard fractional sum by use of the time-scale theory. Then a h-fractional difference is given and fundamental theorems are proved. Initial value problems of fractional difference equations are presented and their equivalent fractional sum equations are provided. The discrete Mittag-Leffler function solutions of linear fractional difference equations are obtained. It can be concluded that the new discrete fractional calculus of Hadamard type is well defined.
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