Integration and differentiation to a variable fractional order. (English) Zbl 0820.26003

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


26A33 Fractional derivatives and integrals
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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[1] Erdelyi A., Higher transcendental functions (1953)
[2] Samko S.G., ”Nauka i Tehnica”, 1987. English Transl.: Fractional integrals and derivatives. Theory and Applications (1992)
[3] Miller K.S., An Introduction to Fractional Calculus and Fractional Differential Equations (1993) · Zbl 0789.26002
[4] DOI: 10.1007/BFb0067095
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