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From Calculus to α- Calculus |
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PP: 411-422 |
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doi:10.18576/pfda/100307
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Author(s) |
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Mohammed Shehata,
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Abstract |
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| In the previous definitions of fractional (α−) calculus, there were a mismatch in some properties to classical calculus. This is because these definitions were built in an unusual way, they were built from the definition of integral to derivative. For example, in the Riemann-Liouville definition of derivative, the derivative of a constant may not be zero. In this paper, we will overcome these incompatibilities, by accurately constructing α− derivative and α− integral by usual way, so it coincides with the classical ones. We also generalized some basic formulas and theorems.
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