The quantification of mineral resources refers to the fractional contribution of endmembers at the pixel level, namely, fraction cover mapping of mineralogy. Over a large area, the mineral deposit occurs generally in a limited number either on a host rock or any geologic structure. In remote sensing, the purity of mineral’s spectra is usually perturbed either because of the weathering effect or the compositional susceptibility, which may lead to a wrong fractional map of mineral endmembers. Having such physical disputes, the present paper establishes a fraction cover mapping model by incorporating the characterization of endmember variability, optimization model of endmember extraction (EE), and inverse model of abundance estimation. In this regard, a proposition of EE method was deployed, which comprises subproblems on the minimization of endmember variability by the alternating direction method. Next, the extracted endmembers were used to estimate abundances with the Hapke model by applying the fully constrained least-squares method. Experimenting on a synthetic image, both the qualitative analysis by correlation measure and quantitative analysis by statistical error measure were evaluated for the proposed fractional cover mapping model. Using airborne visible/infrared imaging spectrometer-next generation hyperspectral imagery, the fraction cover map of a validation area was justified first, then a distributed mapping of Jahazpur-mineralized belt was achieved by the MapReduce programming of the proposed model in Hadoop architecture.