Professor Achar’s current interests are in applications of Fractional Calculus to Physics. He has done pioneering work in this area, developing the theory of fractional oscillators, fractional mechanics of particles including motion under gravity. He has studied intrinsic dissipation in fractional order systems and developed microscopic approach to the theory of fractional viscoelasticity and a path integral approach to fractional quantum mechanics.

Another area of current interest is in the application of Planetarium Software to study ancient astronomy, particularly ancient astronomy of India. Planetarium software can project the view of the sky at any time and at any place in the world. Ancient Sanskrit texts of India such as the Vedas and the Epics contain a lot of astronomical information. With suitable interpretation, the Planetarium software can be advantageously used to determine the dates of these texts. This has led to major contributions to the study of ancient civilization of India.  

Details can be gathered from the list of publications in the last dozen years.