The accurate recognition of a brain tumor (BT) is crucial for accurate diagnosis, intervention planning, and the evaluation of post-intervention outcomes. Conventional methods of manually identifying and delineating BTs are inefficient, prone to error, and time-consuming. Subjective methods for BT recognition are biased because of the diffuse and irregular nature of BTs, along with varying enhancement patterns and the coexistence of different tumor components. Hence, the development of an automated diagnostic system for BTs is vital for mitigating subjective bias and achieving speedy and effective BT segmentation. Recently developed deep learning (DL)-based methods have replaced subjective methods; however, these DL-based methods still have a low performance, showing room for improvement, and are limited to heterogeneous dataset analysis. Herein, we propose a DL-based parallel features aggregation network (PFA-Net) for the robust segmentation of three different regions in a BT scan, and we perform a heterogeneous dataset analysis to validate its generality. The parallel features aggregation (PFA) module exploits the local radiomic contextual spatial features of BTs at low, intermediate, and high levels for different types of tumors and aggregates them in a parallel fashion. To enhance the diagnostic capabilities of the proposed segmentation framework, we introduced the fractal dimension estimation into our system, seamlessly combined as an end-to-end task to gain insights into the complexity and irregularity of structures, thereby characterizing the intricate morphology of BTs. The proposed PFA-Net achieves the Dice scores (DSs) of 87.54%, 93.42%, and 91.02%, for the enhancing tumor region, whole tumor region, and tumor core region, respectively, with the multimodal brain tumor segmentation (BraTS)-2020 open database, surpassing the performance of existing state-of-the-art methods. Additionally, PFA-Net is validated with another open database of brain tumor progression and achieves a DS of 64.58% for heterogeneous dataset analysis, surpassing the performance of existing state-of-the-art methods.