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Zbl 0820.26003
Samko, Stefan G.; Ross, Bertram
Integration and differentiation to a variable fractional order. (English)
[J] Integral Transforms Spec. Funct. 1, No.4, 277-300 (1993). ISSN 1065-2469; ISSN 1476-8291/e

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

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
31B10 Integral representations of harmonic functions (higher-dimensional)
42A38 Fourier type transforms, one variable

Keywords: Riemann-Liouville fractional derivative; Marchaud fractional derivative; variable order; Fourier transforms; inversion formula

Cited in: Zbl 1062.26007 Zbl 0958.26005

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