tijdfractionele

Tijdfractionele, a Dutch term, translates to "time fractional" in English. It refers to a mathematical concept that extends the idea of differentiation and integration to non-integer orders. While traditional calculus deals with integer-order derivatives (like the first derivative, second derivative, etc.), fractional calculus allows for derivatives and integrals of orders that are not whole numbers, such as 0.5 or 1.7.

This concept has found applications in various scientific and engineering fields where phenomena exhibit memory or hereditary effects. For instance, in physics, it can be used to model anomalous diffusion, viscoelastic materials, and wave propagation in complex media. In biology, fractional calculus has been explored for modeling biological tissues and complex biological systems.

The mathematical formulation of fractional derivatives and integrals can be achieved through several definitions, including the Riemann-Liouville definition and the Caputo definition. Each definition has its own advantages and disadvantages depending on the specific problem being addressed. The development of fractional calculus has provided a more sophisticated toolset for describing and analyzing systems that cannot be adequately represented by classical integer-order differential equations.