Research Projects

Fractional order dynamical systems have become a prominent research area due to their diverse applications in interdisciplinary fields. International researchers like Prof. Michele Caputo, Prof. Mauro Fabrizio, Prof. Dumitru Baleanu, Prof. Juan J. Nieto, and Prof. Abdon Atangana have contributed to the field with new mathematical theory and efficient algorithms for numerical system solutions. Indian scientists, such as Prof. Sachin K. Bhalekar, Prof. Subir Das, Devendra Kumar, and Jagdev Singh, have also made significant contributions to this emerging area. However, most fractional order (FO) systems in modeling are derived from their integer order (IO) counterparts, leading to dimensionally non-homogeneous systems. This ambiguity is explained in the main project proposal through the logistic population model. This project aims to develop new fractional order systems that are dimensionally homogeneous, as previous attempts have failed. The project proposes a class of dimensionally fractional order dynamical systems applied in population dynamics and epidemiology, investigating the systems with respect to the fractional order $\alpha$, which could be a bifurcation parameter that changes global stability. The project also explores how period-doubling route to chaos, Neimark-Sacker/Hopf bifurcation and Feigenbaum scenarios, multistabilty, and torus-doubling phenomenon are generated in continuous and discrete fractional order systems. The project serves as a platform to showcase views and encourage others to implement their modeling strategy.