TEMPERED FRACTIONAL CALCULUS ON TIME SCALE FOR DISCRETE-TIME SYSTEMS

Hui Fu (), Lan-Lan Huang (), Thabet Abdeljawad and Cheng Luo ()
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Hui Fu: Data Recover Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
Lan-Lan Huang: Data Recover Key Laboratory of Sichuan Province, College of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, P. R. China
Thabet Abdeljawad: Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia
Cheng Luo: School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 08, 1-9

Abstract: The fractional derivative holds historical dependence or non-locality and it becomes a powerful tool in many real-world applications. But it also brings error accumulation of the numerical solutions as well as the theoretical analysis since many properties from the integer order case cannot hold. This paper defines the tempered fractional derivative on an isolated time scale and suggests a new method based on the time scale theory for numerical discretization. Some useful properties like composition law and equivalent fractional sum equations are derived for theoretical analysis. Finally, numerical formulas of fractional discrete systems are provided. As a special case for the step size h = 1, a fractional logistic map with two-parameter memory effects is reported.

Keywords: Chaos; Time Scale; Tempered Fractional Derivative (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0218348X21400338

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