Improving cell coverage and network capacity are main issues in LTE networks. By the emergence of heterogeneous cellular networks with different cell size, femtocells have been regarded as a low cost solution to improve poor indoor coverage for home users. However, as Femto Access Points (FAPs) are installed by users, self-organized techniques are needed for allocation of radio resources to femtocells. On the other hand, Fractional Frequency reuse (FFR) has been considered to improve spectral efficiency and quality of edge users in heterogeneous networks (HetNets). In conventional FFR methods, the macrocell area is partitioned into some regions and certain fractions of radio resources are considered for macrocell/femtocell users in each region. Therefore, radio resources are allocated to femtocell/macrocell users based on their region of presence without addressing the density of users in that region and consequently the interference level. In this paper, a new self-organized fractional resource allocation method is proposed for femtocells. The proposed method is based on Learning Automata where FAPs learn to choose the best fraction based on the feedback of femtocell users. Simulation results confirm that the proposed radio resource allocation method improves spectral efficiency and decreases the outage probability compared to conventional Strict FFR method.