Akhtar, Nasim2017-08-102023-10-202017-08-102023-10-202016ROLL NO.11612310https://gyan.iitg.ac.in/handle/123456789/822Supervisor: M. Guru Prem PrasadA fractal set is a union of many smaller copy of itself and it has a highly irregular structure. Using Hutchinson's operator, Barnsley [6], introduced Fractal Interpolation Function (FIF) via certain Iterated Function System (IFS). The FIF is continuous and self-a ne in nature. By de ning IFS suitably, one can construct various form of fractal functions including non-self-a ne and partially self-a ne (and partially non-self-a ne) FIFs. For any continuous function f, the corresponding fractal analogue f is non-selfa ne, continuous, nowhere di erentiable function [62,63].enMATHEMATICSThesis