New discretization of Caputo-Fabrizio derivative

被引：30

作者：

Akman, Tugba ^{[1
]}

Yildiz, Burak ^{[2
]}

Baleanu, Dumitru ^{[3
,4
]}

机构：

[1] Univ Turkish Aeronaut Assoc, Dept Management, TR-06790 Ankara, Turkey

[2] Hurma Mah 252,Sok 2-5, Antalya, Turkey

[3] Cankaya Univ, Dept Math, TR-06530 Ankara, Turkey

[4] Inst Space Sci, Magurele 077125, Romania

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 03期

关键词：

Caputo-Fabrizio derivative; Fractional differentiation; L1; formula; L1-2; Quadratic interpolation; SINGULAR KERNEL; DIFFUSION; EQUATION; MODEL;

D O I：

10.1007/s40314-017-0514-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive a numerical approximation, namely L1-2 formula, to the Caputo-Fabrizio derivative by using a quadratic interpolation. Quadratic and cubic convergence rates are achieved for L1 and L1-2 formulas using Lagrange interpolation, respectively. We compute Caputo-Fabrizio derivatives of some known functions both theoretically and numerically. In addition, we solve non/linear sub-diffusion equations to test theoretical findings. Numerical results confirm the theoretically observed convergence rates.

引用

页码：3307 / 3333

页数：27

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