Deep neural networks have demonstrated highly competitive performance in super-resolution (SR) for natural images by learning mappings from low-resolution (LR) to high-resolution (HR) images. However, hyperspectral super-resolution remains an ill-posed problem due to the high spectral dimensionality of the data and the scarcity of available training samples. Moreover, existing methods often rely on large models with a high number of parameters or require the fusion with panchromatic or RGB images, both of which are often impractical in real-world scenarios. Inspired by the MobileNet architecture, we introduce a lightweight depthwise separable dilated convolutional network (DSDCN) to address the aforementioned challenges. Specifically, our model leverages multiple depthwise separable convolutions, similar to the MobileNet architecture, and further incorporates a dilated convolution fusion block to make the model more flexible for the extraction of both spatial and spectral features. In addition, we propose a custom loss function that combines mean squared error (MSE), an L2 norm regularization-based constraint, and a spectral angle-based loss, ensuring the preservation of both spectral and spatial details. The proposed model achieves very competitive performance on two publicly available hyperspectral datasets, making it well-suited for hyperspectral image super-resolution tasks. The source codes are publicly available at: \href{https://github.com/Usman1021/lightweight}{https://github.com/Usman1021/lightweight}.