The Pedagogical Agents (PAs) for Mobile Learning (m-learning) must be able not only to adapt the teaching to the learner knowledge level and profile but also to ensure the pedagogical efficiency within unpredictable changing runtime contexts. Therefore, to deal with this issue, this paper proposes a Context-aware Self-Adaptive Fractal Component based Generalized Pedagogical Agent (CASA FBGPA) framework for Mobile Learning. The proposed framework allows for the construction of PA that self-reconfigures its structure, the functional part, to conform to the unpredictable changing runtime context. To carry out the context-awareness, the PA embeds a distinct Search based Adapting Engine that dynamically monitors and assembles the appropriate linear combination of Fractal components. In addition, to avoid the rules associated conceptual holes, to deal with the conflicting objectives and to reduce the substantial overhead, the components selection is formulated as a multiobjective problem and it is tackled using a metaheuristic search method. Furthermore, to evaluate the design and the feasibility of the proposed framework, a use case and a discussion are provided.