A new Leibniz rule and its integral analogue for fractional derivatives
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Bibliographic record
Abstract
Abstract In 1972, T.J. Osler proposed a generalization of the Leibniz rule for the fractional derivatives of the product of two functions with respect to an arbitrary function. This new rule was based on one of his own result on Taylor's series for the fractional derivative he obtained in 1971. Later, he gave the integral analogue of that new Leibniz rule. In this paper, we present a new Leibniz rule for the fractional derivatives of the product of two functions with respect to an arbitrary function and we give its integral analogue. Finally, new series expansions and definite integrals involving special functions are derived as special cases of the new Leibniz rule and the corresponding integral analogue. Keywords: Leibniz ruleintegral analoguefractional derivativespower seriesspecial functions
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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