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Fractional Mathematical Operators and Their Computational Approximation

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  • José Crespo
  • Francisco Javier Montáns

Abstract

Usual applied mathematics employs three fundamental arithmetical operators: addition, multiplication, and exponentiation. However, for example, transcendental numbers are said not to be attainable via algebraic combination with these fundamental operators. At the same time, simulation and modelling frequently have to rely on expensive numerical approximations of the exact solution. The main purpose of this article is to analyze new fractional arithmetical operators, explore some of their properties, and devise ways of computing them. These new operators may bring new possibilities, for example, in approximation theory and in obtaining closed forms of those approximations and solutions. We show some simple demonstrative examples.

Suggested Citation

  • José Crespo & Francisco Javier Montáns, 2016. "Fractional Mathematical Operators and Their Computational Approximation," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-11, September.
    • Handle: RePEc:hin:jnlmpe:4356371
    DOI: 10.1155/2016/4356371
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