Advanced receptor models can leverage the information derived from optical and chemical variables as input by a variety of instruments at different time resolutions to extract the source specific absorption Ångström exponent (AAE) from aerosol absorption. The multilinear engine (ME-2), a Positive Matrix Factorization (PMF) solver, serves as a proficient tool for performing such analyses, thereby overcoming the constraints imposed by the assumptions in current optical source apportionment methods such as the Aethalometer approach since the use of a-priori AAE values introduces additional uncertainty into the results of optical methods. Comprehensive PM2.5 chemical speciation datasets, and aerosol absorption coefficients (babs, λ) at seven wavelengths measured by an Aethalometer (AE33), were used in multi-time source apportionment (MT-PMF). The study focused on two locations in the Los Angeles (LA) Basin: Central LA (CELA, Main St.), an urban area surrounded by major freeways, and Rubidoux (RIVR), a residential area surrounded by local roads. Factor profiles and temporal variations of their contributions were obtained. Additionally, factor displacements (DISP) and profile constraints were applied. Five-factor solutions were obtained at both sites. At CELA, the resolved factors included traffic + crustal matter (traffic+ Cr_M), secondary sulfate + nitrate (SSN), biomass burning (BB), diesel emissions (DIE) and aged sea salt (ASS). Moreover, source-dependent AAE values at CELA were obtained without a-priori assumption, with values of 1.46 for traffic+ Cr_M, 1.45 for DIE and 2.37 for BB. At RIVR, the resolved factors were traffic+ Cr_M (AAE = 1.24), particulate sulfate, particulate nitrate, BB (AAE = 3.00) and aged sea salt. PM2.5 composition differed at both locations. SSN accounted for the largest fraction of the ambient PM2.5 mass concentration, their sum at the CELA site averaged 40 % of the PM2.5 mass while the same species represented 77 % at RIVR.