# Finite-Difference Methods for Fractional Differential Equations of Order 1/2

## Abstract

In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.

- Authors:

- Mari State University, Department of Physics and Mathematics (Russian Federation)
- M. V. Lomonosov Moscow State University, Scientific Research Computer Center (Russian Federation)
- Instituto Nazionale di Fisica Nucleare, Department of Mathematics and Physics (Italy)

- Publication Date:

- OSTI Identifier:
- 22771254

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 6; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; CONVERGENCE; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; TIME RESOLUTION

### Citation Formats

```
Kokurin, M. Yu., E-mail: kokurinm@yandex.ru, Piskarev, S. I., E-mail: piskarev@gmail.com, and Spreafico, M., E-mail: mauro.spreafico@unisalento.it.
```*Finite-Difference Methods for Fractional Differential Equations of Order 1/2*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3800-6.

```
Kokurin, M. Yu., E-mail: kokurinm@yandex.ru, Piskarev, S. I., E-mail: piskarev@gmail.com, & Spreafico, M., E-mail: mauro.spreafico@unisalento.it.
```*Finite-Difference Methods for Fractional Differential Equations of Order 1/2*. United States. doi:10.1007/S10958-018-3800-6.

```
Kokurin, M. Yu., E-mail: kokurinm@yandex.ru, Piskarev, S. I., E-mail: piskarev@gmail.com, and Spreafico, M., E-mail: mauro.spreafico@unisalento.it. Tue .
"Finite-Difference Methods for Fractional Differential Equations of Order 1/2". United States. doi:10.1007/S10958-018-3800-6.
```

```
@article{osti_22771254,
```

title = {Finite-Difference Methods for Fractional Differential Equations of Order 1/2},

author = {Kokurin, M. Yu., E-mail: kokurinm@yandex.ru and Piskarev, S. I., E-mail: piskarev@gmail.com and Spreafico, M., E-mail: mauro.spreafico@unisalento.it},

abstractNote = {In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.},

doi = {10.1007/S10958-018-3800-6},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 6,

volume = 230,

place = {United States},

year = {2018},

month = {5}

}

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