In 1695, Leibniz wrote about the meaning of the half-order derivative in his message to L ’H ôpital. The foundations of calculus were developed by Newton and Leibniz in the seventeenth century, with differentiation and integration of integer order being the two fundamental operations of this subject. So it extends our possibilities to describe a new set of physical phenomena and improve the accuracy of already-existing models. In a few words: Fractional calculus is able to generalize any integral or differential equation into an infinite set of its "fractional" analogs (where fractional-order integrals and derivatives are involved). So realizing the importance and potential of this topic, functions have been developed for exploring the fractional calculus ecosystem in the Wolfram Language. A lot of scientific phenomena are described with fractional differential, integral and mixed-type equations. This branch is becoming more and more popular in diffusion problems, fluid dynamics, control theory, signal processing and other areas. įractional calculus is not just a pure mathematical theory. It extends the classical calculus basic operations to fractional orders and studies the methods of solving differential equations involving these fractional-order derivatives and integrals. Definitions of Fractional Differintegralsįractional Differintegrals in the Wolfram Languageįractional calculus develops the theory of differentiation and integration of any real or complex order.
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