Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives

TL;DR

This paper demonstrates how initial conditions involving Riemann-Liouville fractional derivatives in fractional differential equations can be given physical meaning and determined through measurements, with applications in viscoelasticity.

Contribution

It provides a method to interpret and measure initial conditions with Riemann-Liouville derivatives in physical systems, bridging theory and practical observation.

Findings

Initial conditions can be physically interpreted in viscoelastic models.

Initial values for fractional derivatives can be obtained through measurements.

The approach enhances the applicability of fractional differential equations in physics.

Abstract

On a series of examples from the field of viscoelasticity we demonstrate that it is possible to attribute physical meaning to initial conditions expressed in terms of Riemann-Liouville fractional derivatives, and that it is possible to obtain initial values for such initial conditions by appropriate measurements or observations.