Fractional differentiation and integration

Applied Mathematics and Computation, 2019
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Mohammad Javidi, Esmail Babolian
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Fractional Integration and Differentiation

2010
In this chapter we deal with “complex powers of the operator \(\frac{d}{{dx}},\)” a concept already found in the posthumous works of Riemann and elaborated by Marcel Riesz in the 1930s and 1940s. The relevant article [18] is lengthy, but with the help of a little distribution theory and complex analysis, all results can readily be proved.We will also ...
J A C Kolk, Duistermaat J J, Kolk J A C
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Integration and differentiation to a variable fractional order

Integral Transforms and Special Functions, 1993
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.
Stefan Samko, Bertram Ross
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Fractional integration and differentiation of variable order

Analysis Mathematica, 1995
The paper deals with the generalized fractional integration and differentiation operators of variable order \(\alpha (x)\): \[ I_+^{\alpha (x)} \varphi= {1\over {\Gamma (\alpha (x))}} \int^x_{-\infty} {{\varphi (t)dt} \over {(x-t)^{1- \alpha(x)}}} \;(\alpha (x)>0) \;\text{ and } \;D_+^{\alpha (x)}= \lim_{\varepsilon \to 0} D^{\alpha (x)}_{+,\varepsilon}
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fractional calculus
mathematics
fractional derivatives and integrals

fractional differential equations
fractional ordinary differential equations
fos: mathematics

fractional integration
qa1-939
generalized mathieuseries