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2. The Weyl fractional integral and the Mellin transform
3. Fractional-order dynamical systems in control theory.
4. Electrical circuits with fractance.
5. Generalized voltage divider
6. Fractional calculus in viscoelasticity.
7. Fractional-order multipoles in electromagnetism
8. Fractional calculus in electrochemistry and tracer fluid flows
9. Fractional-order model of neurons in biology.
10. Numerical computation of fractional derivatives and integrals.
1. INTRODUCTION TO FRACTIONAL CALCULUS
2. FRACTIONAL INTEGRAL EQUATIONS
3. FRACTIONAL DIFFERENTIAL EQUATIONS: 1-st PART
4. FRACTIONAL DIFFERENTIAL EQUATIONS: 2-nd PART
APPENDIX : THE MITTAG-LEFFLER TYPE FUNCTIONS
Applications to transport in fusion plasmas
Some limitations of the RL definition
Behavior near the lower terminal
Caputo fractional derivative
Nonlocal transport model
Local and non-local transport
Nonlocal transport and global diffusive coupling
Confinement time scaling
“Up-hill” transport and pinch velocity
Fractional flux asymmetry and pinch velocity
“Cold-pulse” fast propagation, Off-axis heating
Application to reactiondiffusion systems
The fractional Fisher-Kolmogorov equation
Asymmetric front dynamics
Right moving algebraic decaying, accelerated front
Leading edge calculation for exponential fronts
Left moving exponential decaying, constant velocity front
Fractional reaction-diffusion systems
Numerical integration of fractional equations
1. Elementary preliminaries
2. Gr ¨unwald’s construction
3. The Riemann-Liouville construction.
4. Further elaborations.
5. Abel’s solution of the tautochrone problem.
6. Heaviside’s solution of the diffusion equation
7. Riesz’ “method of dimensional ascent.”
8. Application to the mensuration of hyperspheres
9. Application to the differention of fractal curves.
10. Charge density on a needle
11. Eigenfunctions of derivative operators of integral/fractional order.
2: THE RIEMANN-LIOUVILLE FRACTIONAL INTEGRAL
3: THE RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE
4: FRACTIONAL DIFFERENTIAL EQUATIONS
5: APPLICATIONS AND THE PUTZER ALGORITHM
CONCLUSION AND FUTURE SCOPE APPENDIX