Dr. Udita Katugampola was recently awarded a Department of Defense (DOD) research grant for his work on fractional derivatives. The single-PI award in the amount of $300,032, will fund his and his students’ research work for the next four years.
The fractional derivatives (FD) are generalizations of familiar integer order derivatives. According to Dr. Katugampola, the concept of the fractional derivative goes back to 1695 when Leibniz introduced the notation (d^n y)/(dx^n ) to L’Hospital. In a reply, L’Hospital asked “What if n = 1/2?", which did not have a satisfactory answer at that time. Nowadays, it is easy to find applications of FDs in pure and applied mathematics, engineering, physics, chemistry, biology, medicine and even in psychology. The idea will enable researchers to find hidden beauties in the nature that cannot otherwise be identified using the classical derivatives. Some of the striking ideas of FDs include the concept of Fractional Brownian Motion, which, for example, governs the stock market, functions in our brain or anomalous diffusion that can be found in many porous medium such as the surface of the sun or inside battery cells. His work on FD will enhance the profound understanding of the field of fractional calculus and enables further applications in real-world situations by redefining the true nature of the realm which once was only available for pure mathematician who work on abstract mathematics.
The proposed research also focuses on some combinatorial aspects of a class of sequences (A223523-A223532 on Sloane’s OEIS) and Fourier analysis which, if successful, will redefine the Nuclear Magnetic Resonance (NMR) techniques. In this part of the research, he, his students and collaborators will work on a derivative, now known as, the Katugampola Fractional Derivative. It is interesting that this is the first time the DOD allocated research funds solely for the purpose of further studies in fractional calculus. There are only a few universities in US that offer graduate studies in FD. According to him, he is also planning to apply for research funds from National Science Foundation (NSF) to further enhance his research work in FD.