# New discretization of Caputo–Fabrizio derivative

## Abstract

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.

- Authors:

- University of Turkish Aeronautical Association, Department of Management (Turkey)
- Hurma Mah. (Turkey)
- Çankaya University, Department of Mathematics (Turkey)

- Publication Date:

- OSTI Identifier:
- 22769277

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; CONVERGENCE; DIFFUSION EQUATIONS; FUNCTIONS; INTERPOLATION; NONLINEAR PROBLEMS

### Citation Formats

```
Akman, Tuğba, Yıldız, Burak, and Baleanu, Dumitru.
```*New discretization of Caputo–Fabrizio derivative*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0514-1.

```
Akman, Tuğba, Yıldız, Burak, & Baleanu, Dumitru.
```*New discretization of Caputo–Fabrizio derivative*. United States. doi:10.1007/S40314-017-0514-1.

```
Akman, Tuğba, Yıldız, Burak, and Baleanu, Dumitru. Sun .
"New discretization of Caputo–Fabrizio derivative". United States. doi:10.1007/S40314-017-0514-1.
```

```
@article{osti_22769277,
```

title = {New discretization of Caputo–Fabrizio derivative},

author = {Akman, Tuğba and Yıldız, Burak and Baleanu, Dumitru},

abstractNote = {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.},

doi = {10.1007/S40314-017-0514-1},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}

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