Fractional diffusion and parametric subordination
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Rudolf Gorenflo
Abstract
In this chapter, we consider simulation of spatially one-dimensional spacetime fractional diffusion. After a survey on the operators entering the basic fractional equation via Fourier-Laplace manipulations, we obtain the subordination integral formula that teaches us how a particle path can be constructed by first generating the operational time from the physical time and then generating in operational time the spatial path. By inverting the generation of operational time from physical time, we arrive at the method of parametric subordination.
Abstract
In this chapter, we consider simulation of spatially one-dimensional spacetime fractional diffusion. After a survey on the operators entering the basic fractional equation via Fourier-Laplace manipulations, we obtain the subordination integral formula that teaches us how a particle path can be constructed by first generating the operational time from the physical time and then generating in operational time the spatial path. By inverting the generation of operational time from physical time, we arrive at the method of parametric subordination.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- Fractional electromagnetics 1
- Fractional electrodynamics with spatial dispersion 25
- Fractional-calculus tools applied to study the nonexponential relaxation in dielectrics 53
- Fractional diffusion-wave phenomena 71
- Fractional diffusion and parametric subordination 99
- The fractional advection-dispersion equation for contaminant transport 129
- Anomalous diffusion in interstellar medium 151
- Fractional kinetics in random/complex media 183
- Nonlocal quantum mechanics: fractional calculus approach 207
- Fractional quantum fields 237
- Fractional quantum mechanics of open quantum systems 257
- Fractional quantum mechanics with topological constraint 279
- Fractional time quantum mechanics 299
- Index 317
