The work presented in this paper aims at enhancing the performance of end-to-end (E2E) speech recognition task for children's speech under low resource conditions. For majority of the languages, there is hardly any speech data from child speakers. Furthermore, even the available children's speech corpora are limited in terms of the number of hours of data. On the other hand, large amounts of adults' speech data are freely available for research as well as commercial purposes. As a consequence, developing an effective E2E automatic speech recognition (ASR) system for children becomes a very challenging task. One may develop an ASR system using adults' speech and then use it to transcribe children's data, but this leads to very poor recognition rates due to the stark differences in the acoustic attributes of adults' and children's speech. In order to overcome these hurdles and to develop a robust children's ASR system employing E2E architecture, we have resorted to several out-of-domain and in-domain data augmentation techniques. For out-of-domain data augmentation, we have explicitly modified adults' speech to render it acoustically similar to that of children's speech before pooling into training. On the other hand, in the case of in-domain data augmentation, we have slightly modified the pitch and duration of children's speech in order to create more data capturing greater diversity. Data augmentation approaches helps in mitigating the ill-effects resulting from the scarcity of data from child domain to a certain extent. This, in turn, reduces the error rates by a large margin. In addition to data augmentation, we have also studied the efficacy of Gamma-tone frequency cepstral coefficients (GFCC) and frequency domain linear prediction (FDLP) technique along with the most commonly used Mel-frequency cepstral coefficients (MFCC) for front-end speech parameterization. Both MFCC as well as GFCC capture and model the spectral envelope of speech. On the other hand, application of linear prediction on the frequency domain representation of speech signal helps to effectively capture the temporal envelope during front-end feature extraction. Employing FDLP features that model the temporal envelope provides important cues for the perception and understanding of stop bursts and, at times, complete phonemes. This motivated us to perform a comparative experimental study of the effectiveness of the three aforementioned front-end acoustic features. In our experimental explorations, the use of proposed data augmentation in combination of FDLP features has shown a relative improvement in character error rate by 67.6% over the baseline system. The combination of data augmentation with MFCC or GFCC features is observed to result in lower recognition performances.