Novel Fractional Models Compatible with Real World Problems
In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modified form of this new definition. We utilize the &...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-04-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/3/2/15 |
| Summary: | In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modified form of this new definition. We utilize the <inline-formula>
<math display="inline">
<semantics>
<mi>σ</mi>
</semantics>
</math>
</inline-formula> auxiliary parameter for preserving the dimension of physical quantities for newly defined fractional conformable vertical motion of a falling body problem in a resistant medium. The analytical solutions are obtained by iterating this new fractional integral and results are illustrated under different orders by comparison with the Liouville–Caputo fractional operator. |
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| ISSN: | 2504-3110 |