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arXiv · 1207.0409

Definitions of real order integrals and derivatives using operator approach

Raoelina Andriambololona
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Abstract

The set E of functions f fulfilling some conditions is taken to be the definition domain of s-order integral operator J^s (iterative integral), first for any positive integer s and after for any positive s (fractional, transcendental π and e). The definition of k-order derivative operator D^k for any positive k (fractional, transcendental π and e) is derived from the definition of J^s. Some properties of J^s and D^k are given and demonstrated. The method is based on the properties of Euler's gamma and beta functions.

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Raoelina Andriambololona. 2013-03-08. Definitions of real order integrals and derivatives using operator approach. https://arxiv.org/abs/1207.0409

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