Index
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additivity 2.2.1.9
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adjoint operators 2.2.1.7
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analysis of singularities 2.2.2.8
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anomalous subdiffusion 2.3.1
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Banach space Appendix B, 2.2.2.6, 2.2.2.9, 2.3.3.2
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Bernstein function 2.3.3.6
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Bessel function 2.3.4.2
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binomial formula 2.1.1, 2.2.2.6
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Bochner-Levy diffusion 2.2.2.9, 2.3.4.1
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Borel measure 2.3.3.6
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Cauchy problem 2.3.3.1
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causality 2.3.3.5
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classification of phase transitions 2.2.2.8
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conjugate Riesz potential Definition 2.3
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continuity in time 2.3.3.3
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continuous time random walk 2.3.4.3
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convolution
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critical phenomena 2.2.2.8
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CTRW 2.3.4.3
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difference quotient 2.1.4, 2.1.4, 2.1.6, 2.2.2.6, 2.2.2.6
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diffusion 2.2.2.9, 2.3.1, 2.3.2, 2.3.2, 2.3.4, 2.3.4.1, 2.3.4.2, 2.3.4.2, 2.3.4.2, 2.3.4.2, 2.3.4.3
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Dirac function Appendix C, Appendix C, Appendix C, 2.2.1.3, 2.2.1.5
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Dirac-measure 2.3.3.6
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distribution(s) Appendix C
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Ehrenfest classification 2.2.2.8
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eigenfunction(s)
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fractional derivatives 2.2.3
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ergodicity breaking 2.3.3.1
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essential range Appendix B
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Euler 2.1.2, 2.1.3
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Euler Beta function 2.2.1.9
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exponential series 2.1.3, 2.1.4
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Fokker-Planck equation 2.3.4.1
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Fourier 2.1.5
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Fourier series 2.2.1.3
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Fourier transformation 2.2.1.6, 2.2.2.5
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fractional derivative
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fractional difference quotient 2.2.2.6
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fractional differential equation 2.2.3, 2.2.3, 2.3.1
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fractional diffusion 2.3.4, 2.3.4.1, 2.3.4.2, 2.3.4.3
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fractional integral 2.2.1
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fractional integration
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fractional master equation 2.3.4.3, 2.3.4.3
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fractional powers 2.2.2.9
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fractional stationarity 2.3.3.8
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fractional time 2.3.3
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fractional time evolution 2.3.3.6
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function(s)
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Gamma function 2.1.2, 2.2.1.2
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Grünwald 2.1.6
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Grünwald-Letnikov derivative 2.2.2.6
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Hardy-Littlewood theorem 2.2.1.8
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Heaviside step function 2.2.1.3
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-function 2.3.3.6, 2.3.4.2
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Hilbert space Appendix B, 2.2.2.9
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Hölder space Appendix B
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homogeneity of time 2.3.3.4
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homogenous divisibilty 2.3.3.4, 2.3.3.6, 2.3.3.8
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Hörmander symbol class Definition 2.19
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identity operator 2.2.2.3, 2.2.2.6
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infinitesimal generator 2.2.2.9, 2.3.3.7
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integral transforms 2.2.1.6
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integration
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integroderivatives 2.1.6
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irreversibility problem
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iterated integrals 2.2.1.1
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Kohn-Nirenberg pseudodifferential operator Definition 2.19
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Laplace transformation 2.2.1.6
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Laplacian 2.2.2.9, 2.3.4.1
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Lebesgue space Appendix B
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Leibniz 2.1.1, 2.1.3
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Leibniz’ paradox 2.1.1, 2.1.2, 2.1.3
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Leibniz’ product rule 2.1.1
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Liouville 2.1.4
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Lizorkin space 2.2.1.6
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local fractional derivative 2.2.2.8
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locality 2.3.2, 2.3.4.2
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locally integrable function Appendix B
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Marchaud fractional derivative 2.2.2.3
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master equation 2.3.4.3
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Mellin transformation 2.3.3.6
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Mittag-Leffler function 2.2.3
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Montroll-Weiss diffusion 2.3.4.2
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nonlocality 2.3.2, 2.3.2, 2.3.3.1, 2.3.3.1
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operator(s)
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-integrable function Appendix B
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principal value Appendix C
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pseudodifferential operators 2.2.2.10
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random walk
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rapidly decreasing function Appendix B
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regularly varying function 2.2.2.8
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Riemann 2.1.7
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Riemann-Liouville derivatives 2.2.2.1
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Riemann-Liouville fractional integrals 2.2.1.2
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Riesz-Feller kernel 2.2.1.4
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Riesz fractional derivatives 2.2.2.5
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Riesz fractional integrals 2.2.1.4
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Riesz kernel 2.2.1.4
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Riesz potential 2.2.1.4
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Schwartz space Appendix B, Appendix C
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semigroup 2.2.1.9, 2.2.2.9, 2.2.2.9, 2.3.3.1, 2.3.3.2, 2.3.3.6, 2.3.3.6, 2.3.3.7
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singularities 2.2.2.8
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slowly varying function 2.2.2.8
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Sobolev space Appendix B
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space
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stationarity 2.3.3.1, 2.3.3.8
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subdiffusion 2.3.1
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test functions Appendix C
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time
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time evolution 2.3.3.2
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translation invariance 2.3.3.1, 2.3.3.4, 2.3.3.6
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translation operator 2.2.2.3, 2.2.2.6
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types of fractional derivative 2.2.2.2
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unit step function 2.2.1.3
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Weyl fractional integrals 2.2.1.3
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Youngs inequality 2.2.1.8