Open AccessTEMPERED FRACTIONAL CALCULUS ON TIME SCALE FOR DISCRETE-TIME SYSTEMS
Author(s) -
Hui Fu,
Lanlan Huang,
Thabet Abdeljawad,
Cheng Luo
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x21400338
Subject(s) - fractional calculus , discretization , mathematics , scale (ratio) , integer (computer science) , discrete time and continuous time , derivative (finance) , locality , order (exchange) , numerical analysis , calculus (dental) , mathematical analysis , computer science , statistics , medicine , linguistics , physics , philosophy , dentistry , finance , quantum mechanics , financial economics , economics , programming language
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 [Formula: see text], a fractional logistic map with two-parameter memory effects is reported.