Abstract:
Even though fractional-order derivatives can easily be seen as a “natural” generalization of integer-order derivatives, their studies have mostly been limited to the mathematics community. This is evident from the fact that despite being as old as the Newtonian calculus, the order of the fractional derivative is mainly obtained by curve-fitting the experimental data with the theoretically predicted curves. A deductive approach to fractional derivatives from real physical processes is still lacking. The physical and geometrical interpretation of the fractional-order has remained an open question for the fractional community and those who use them to describe the anomalous behaviour of complex media. Consequently, fractional calculus has been plagued as an “empirical-only” mathematical methodology. This talk aims to present the physics underlying power-law behaviour in complex media and hence a deductive approach to the fractional derivatives. When derived from the first principles of physics, the fractional-order gains physical interpretation. A few examples of this are the derivation of four empirical laws for the first time; Omori's law of earthquake-aftershocks, Andrade's law of universal creep, Nutting’s law in rheology, and Lomnitz’s creep law in seismology. The physics underlying the four laws had been missing since their inception in 1894, 1910, 1921, and 1956 respectively. The overall goal is to show that fractional calculus is not just a mathematical framework that can only be empirically introduced to curve-fit the experimental observations. Rather, it has an inherent connection to real physical processes that need to be explored more.
Short-bio:
Vikash Pandey is a mathematical physicist, and his research interests are pretty interdisciplinary, with a primary focus on the physics of complex systems and the resulting memory-driven emergent power-law behavior. After receiving M.Sc degree in Physics from the Banaras Hindu University, Varanasi, he worked as a geophysicist for a seismic company in US, UK, and Africa. After that, he earned his Ph.D. degree from the University of Oslo, Norway, in 2016. He did his postdoctoral research at the University of Oslo, and UiT, The Arctic University of Norway in Tromsø. His publications encompass the fields of fractional calculus, acoustics, fractal geometry, viscoelasticity, non-Newtonian rheology, dielectrics, and nonlinear bubble dynamics. Identifying the underlying mechanism of observed physical phenomena and the ability to describe them with an appropriate mathematical formulation gives him unmatched joy. His long-term research goal is to extend the applications of fractional calculus to the traditional branches of physics, such as quantum physics and cosmology. His hobbies are hiking, trekking, bird-watching, and motorcycling.