This paper proposes a novel Agentic Retrieval-augmented generation with Mamba-Attention Integrated Transformer (ARMAIT) framework for multi-Unmanned Aerial Vehicle (UAV) trajectory optimization. The framework is built upon Large Language Models (LLMs), incorporating Retrieval-Augmented Generation (RAG) empowered by Agentic AI and integrated with a UAV-specific knowledge base. Through the Agentic RAG, the LLM autonomously interprets high-level task requirements and identifies the key components necessary for trajectory optimization, including model inputs and outputs, network architecture, reward functions, and task constraints. To support efficient modeling across different system scales, we introduce the Mamba-Attention Integrated Transformer (MAIT), a hybrid neural architecture that combines the long-range dependency modeling capability of attention mechanisms with the efficient temporal dynamic representation of Mamba. Furthermore, a Trajectory-Group Relative Policy Optimization (T-GRPO) method is proposed to achieve unified policy gradient optimization in both discrete and continuous trajectory spaces for MAIT training. Extensive experimental results validate the feasibility and effectiveness of the proposed ARMAIT framework.