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Fractional Derivative and Fractional Integral
2018For every α > 0 and a local integrable function f(t), the right FI of order α is defined: $$\displaystyle{ }_aI_t^\alpha f(t) = \displaystyle\frac {1}{\Gamma (\alpha )}\displaystyle\int _a^t(t - u)^{\alpha - 1}f(u)du,\qquad-\infty \le a < t < \infty .$$
Constantin Milici +2 more
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Probability Theory and Related Fields, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dasgupta, A., Kallianpur, G.
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dasgupta, A., Kallianpur, G.
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Multilinear Singular and Fractional Integrals
Acta Mathematica Sinica, English Series, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ding, Yong, Lu, Shanzhen, Yabuta, Kôzô
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2002
A new class of fractional integrals connected with balls in R n was introduced and investigated by B. Rubin in [246] (see also [247]). The special interest in ball fractional integrals (BFI’s) arises from the fact that Riesz potentials I a f over a ball B may be represented by a composition of such integrals.
David E. Edmunds +2 more
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A new class of fractional integrals connected with balls in R n was introduced and investigated by B. Rubin in [246] (see also [247]). The special interest in ball fractional integrals (BFI’s) arises from the fact that Riesz potentials I a f over a ball B may be represented by a composition of such integrals.
David E. Edmunds +2 more
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Fractional Chern insulators in magic-angle twisted bilayer graphene
Nature, 2021Yonglong Xie +2 more
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Signatures of fractional quantum anomalous Hall states in twisted MoTe2
Nature, 2023, Eric Anderson, Chong Wang
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Thermodynamic evidence of fractional Chern insulator in moiré MoTe2
Nature, 2023, Patrick Knüppel, Kenji Watanabe
exaly
2013
This chapter introduces the reader to a collection of problems that are rarely seen: the evaluation of exotic integrals involving a fractional part term, called fractional part integrals. The problems were motivated by the interesting formula \(\int _{0}^{1}\left \{1/x\right \}\mathrm{d}x = 1-\gamma ,\) which connects an exotic integral to the Euler ...
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This chapter introduces the reader to a collection of problems that are rarely seen: the evaluation of exotic integrals involving a fractional part term, called fractional part integrals. The problems were motivated by the interesting formula \(\int _{0}^{1}\left \{1/x\right \}\mathrm{d}x = 1-\gamma ,\) which connects an exotic integral to the Euler ...
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Observation of fractional edge excitations in nanographene spin chains
Nature, 2021Shantanu Mishra +2 more
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Fractionally Differenced and Fractionally Integrated Processes
2016The adjective “fractional” appears frequently in the names of processes related to long-range dependence; two immediate examples are the fractional Brownian motion of Example 3.5.1 and the fractional Gaussian noise introduced in Section 5 ...
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