HADAMARD FRACTIONAL CALCULUS ON TIME SCALES

Ting-Ting Song, Guo-Cheng Wu and Jia-Li Wei
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Ting-Ting Song: School of Mathematical Sciences, Bohai University, Jinzhou 121013, P. R. China2Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
Guo-Cheng Wu: Data Recovery Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
Jia-Li Wei: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu Province, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 07, 1-14

Abstract: 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.

Keywords: Hadamard Fractional Derivative; Discrete Fractional Calculus; Time Scales (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0218348X22501456

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