Fractional paradigm

By generalization, we mean the extension of the domain of some of the arguments of a function. By arbitrary order, we mean that we are extending this domain from the set of natural numbers or integers to the set of real or complex numbers.

This is done in order to develop more powerful tools, from the currently existing ones, that can describe a wider range of observed phenomena.

It is referred to as a paradigm because it is not a particular method, but rather an abstract intellectual tool or idea, used to develop methods of approaching novel problems. The terminology "paradigm" also refers to the implied ontological assumption that continuous functions are more fundamental than discrete ones. i.e. that when one "fractionalizes", one is not merely posturing a phenomenological "curve fitting", but rather uncovering a more direct description of reality.

Related topics

• fractionalization of operators[?]
• fractional calculus
• fractional probability
• fractional electromagnetics[?]