Autism spectrum disorder (ASD) is a neurodevelopmental disorder with a deficit of social relationships, interaction, sense of imagination, and constrained interests. Early diagnosis of ASD will aid in devising appropriate training procedures and placing those children in the normal stream. The objective of this research is to analyze the brain response for auditory/visual stimuli in Typically Developing (TD) and children with autism through electroencephalography (EEG). Brain dynamics in the EEG signal can be analyzed well with the help of nonlinear feature primitives. Recent research reveals that, application of fractal-based techniques proves to be effective to estimate of degree of nonlinearity in a signal. This research attempts to analyze the effect of brain dynamics with Higuchi Fractal Dimension (HFD). Also, the performance of the fractal based techniques depends on the selection of proper hyper-parameters involved in it. One of the key parameters involved in computation of HFD is the time interval parameter ‘k’. Most of the researches arbitrarily fixes the value of ‘k’ in the range of all channels. This research proposes an algorithm to estimate the optimal value of the time parameter for each channel. Sub-band analysis was also carried out for the responding channels. Statistical analysis on the experimental reveals that a difference of 30% was observed between autistic and Typically Developing children.