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New approach to the fractional derivatives

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  • Kostadin Trenčevski

Abstract

We introduce a new approach to the fractional derivatives of the analytical functions using the Taylor series of the functions. In order to calculate the fractional derivatives of f , it is not sufficient to know the Taylor expansion of f , but we should also know the constants of all consecutive integrations of f . For example, any fractional derivative of e x is e x only if we assume that the n th consecutive integral of e x is e x for each positive integer n . The method of calculating the fractional derivatives very often requires a summation of divergent series, and thus, in this note, we first introduce a method of such summation of series via analytical continuation of functions.

Suggested Citation

  • Kostadin Trenčevski, 2003. "New approach to the fractional derivatives," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-11, January.
    • Handle: RePEc:hin:jijmms:647423
    DOI: 10.1155/S0161171203206050
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