Two definitions of fractional derivative of powers functions

Details Two definitions of fractional derivative of powers functions Two definitions of fractional derivative of powers functions

2012-04-05

arxiv.org/abs/1204.1493v1

Mathematics

General Mathematics

22 pages

Scientific paper

We consider the set of powers functions, defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders. We give the properties of linearity and commutativity and the notions of semi-equality, semi-linearity and semi-commutativity are introduced. Our approach gives a unified definition of the common derivatives and integrals and their generalization.

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