Hyperspectral sensors have high spectral resolution by capturing images in hundreds of bands. Despite the high spectral resolution, low spatial resolution of these sensors restricts the performance of the hyperspectral imaging applications such as target tracking and image classification. Fusing the hyper-spectral image (HSI) with higher spatial resolution RGB or multispectral image (MSI) data is a commonly used method in the resolution enhancement of the HSIs. In this paper, we propose a new fusion technique for the HSI super-resolution. The main contribution of this study is formulating the fusion problem in a quadratic manner and also regularizing the solution quadratically using smoothness prior. Moreover, another contribution of the proposed method is converting the fusion problem from spectral domain to the abundance map domain which gives more robust and spectrally consistent results. In the proposed method, first, abundance maps are obtained using linear spectral unmixing and then a quadratic energy function is obtained using these maps and high resolution (HR) RGB image. In addition, quadratic function is regularized using additional constraints. Solving the regularized quadratic function gives the HR abundance maps and these maps are used to reconstruct HR HSI. Experiments show that proposed method yields better performance as compared to state of the art methods in different performance metrics.