Fractional calculus: Applications
The invention of differential calculus by Leibniz and Newton allowed modeling of dynamical processes. The fractional calculus allows making a revolutionary step towards better models of reality.
General view
- G.W. Scott Blair (1950):
- “We may express our concepts in Newtonian
terms if we find this convenient but, if we do so,
we must realize that we have made a translation
into a language which is foreign to the system
which we are studying.”
- S. Westerlund (1991):
- “Expressed differently, we may say that
Nature works with fractional time derivatives.”
- K. Nishimoto (1989):
- “The fractional calculus is the calculus of the XXI-st century.”
Fields of applications
- New mathematical models of real materials. Viscoelasticity. Aftereffects.
- Modeling od hereditary processes. Ageing of materials and systems.
- Dynamical processes in fractals. Diffusion and other transfer processes in fractals.
- Fractional-order controllers. PIλDμ-controllers, CRONE controllers. Active noise control.
- Mathematical models in economy. Econophysics.
- New types of electrical circuits. Fractances.
- Physiology. Models of live tissues.
- Chemistry. Electrochemistry. Voltammetry. Polarography.
Special journal issues on fractional calculus and its applications
- Fractional Differential Systems: Models, Methods and Applications. ESAIM Proceedings, Vol. 5, 1998, 1-204.
- Special Issue of Fractional Order Calculus and Its Applications.
Nonlinear Dynamics, July–September 2002, Volume 29, Issue 1-4.
- Special Issue on Strange Kinetics.
Chemical Physics, Volume 284, Issues 1-2,
Pages 1-541 (1 November 2002).
- Special Issue on Fractional Signal Processing and Applications. Signal Processing, Volume 83, Issue 11, Pages 2285-2480 (November 2003).
- Special Issue of Fractional Order Derivatives and their Applications.
Nonlinear Dynamics, December 2004, Volume 38, Issue 1-2.
- New: Special Issue on Fractional Calculus Applications in Signals and Systems
Signal Processing, Volume 86, Issue 10, Pages 2503-3094 (October 2006)