Abstract
In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended fractional derivatives of some elementary functions are calculated. At the same time, extensions of some hypergeometric functions and their integral representations are presented by using the extended fractional derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained, and Mellin transforms of some extended fractional derivatives are also determined.
| Original language | English |
|---|---|
| Pages (from-to) | 3611-3621 |
| Number of pages | 11 |
| Journal | Journal of Nonlinear Science and Applications |
| Volume | 9 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2016 |
| Externally published | Yes |
Keywords
- Caputo fractional derivative
- Generating functions
- Hypergeometric functions
- Integral representations
- Mellin transform
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