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December 1, 1993Integral Transforms and Special Functions612 citations

Integration and differentiation to a variable fractional order

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SSStefan SamkoTbilisi State UniversityBRBertram RossUniversity of New Haven

Key Points

  • The aim is to explore the interpretation and differentiation of functions to a variable fractional order.
  • Studied differentiation using the Riemann-Liouville definition
  • Explored properties with Fourier transforms
  • Derived an inversion formula for fractional order differentiation.
  • Properties of fractional order differentiation are established.
  • An inversion formula is obtained for the discussed methods.

Abstract

Interpretation and differentiation of functions to a variable order (d/dx)nf(x) is studied in two ways: 1) using the Riemann-Liouville definition, 2) using Fourier transforms. Some properties and the inversion formula are obtained.

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Cite This Study

Samko et al. (1993) studied this question.

synapsesocial.com/papers/69d8cc20b0225cae72bedc36https://doi.org/10.1080/10652469308819027
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