The twin extreme learning machine (TELM), based on the hinge-loss function, demonstrates significant potential for pattern classification tasks. However, the hinge-loss function, which minimizes the shortest distance between sets, results in classifiers that are sensitive to noise and unstable in the presence of overfitting. To enhance TELM's performance, a novel learning framework, termed adaptive fractional loss TELM (AFTELM), is proposed. This framework incorporates an adaptive fractional loss (AF-loss) function, offering improved robustness to noise compared to TELM with hinge loss. A theoretical analysis is provided to examine the noise insensitivity of AFTELM. The concave-convex procedure (CCCP) is employed for efficient optimization. Extensive experiments on benchmark datasets validate the superior performance of AFTELM, demonstrating its robustness to noise and enhanced classification ability.