NUMERICAL METHODS FOR THE CAPUTO-TYPE FRACTIONAL DERIVATIVE WITH AN EXPONENTIAL KERNEL

Enyu Fan; Changpin Li; Zhiqiang Li

doi:10.11948/20220177

2023 Volume 13 Issue 1

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Enyu Fan, Changpin Li, Zhiqiang Li. NUMERICAL METHODS FOR THE CAPUTO-TYPE FRACTIONAL DERIVATIVE WITH AN EXPONENTIAL KERNEL[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 376-423. doi: 10.11948/20220177

Citation:

Enyu Fan, Changpin Li, Zhiqiang Li. NUMERICAL METHODS FOR THE CAPUTO-TYPE FRACTIONAL DERIVATIVE WITH AN EXPONENTIAL KERNEL[J]. Journal of Applied Analysis & Computation, 2023, 13(1): 376-423. doi: 10.11948/20220177

NUMERICAL METHODS FOR THE CAPUTO-TYPE FRACTIONAL DERIVATIVE WITH AN EXPONENTIAL KERNEL

1.
Department of Mathematics, Shanghai University, Shanghai 200444, China
2.
Department of Mathematics, Lvliang University, Lvliang 0033001, China

Corresponding author: Email: lcp@shu.edu.cn(C. Li)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 12271339)

Abstract

Abstract

In the present article, several typical numerical discrete formulas for the Caputo-type fractional derivative with an exponential kernel (call "exponential Caputo derivative" for brevity) with order $ \alpha\in(0,1) $ and $ \alpha\in(1,2) $ are constructed, which are L1, L1-2, L2-1$ _\sigma $ formulas for $ \alpha\in(0,1) $, and H2N2 and L2$ _{1} $ formulas for $ \alpha\in(1,2) $, respectively. And the estimates of the truncation errors are determined. Meanwhile, the properties of the coefficients in these formulas are studied. Finally, some numerical examples are displayed which support the theoretical analysis.
- Exponential Caputo derivative /
- numerical discrete formula /
- truncation error
MSC: 26A33, 65D25

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References

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