This study delves into the exploration of various types of fractional integro-differential equations (FIDEs) through a direct fractional calculus approach, aiming to provide a comprehensive understanding of their solutions. The method employed not only yields diverse and significant outcomes but also extends beyond the conventional Frobenius method, offering novel insights into solving FIDEs efficiently. It primarily relies on fundamental theorems addressing specific solutions, including the Mahgoub transform and extension coefficients derived from binomial series, showcasing the versatility of fractional calculus techniques. Additionally, advanced strategies for solving FIDEs effectively are presented, incorporating innovative computational methods and integral transforms. Moreover, the research introduces advanced solution methodologies, emphasizing their practical applicability through a range of illustrative examples across various fields such as engineering, physics, and finance. By bridging theoretical advancements with practical relevance, this study contributes to the broader understanding and utilization of fractional calculus in addressing complex differential equations, offering valuable insights for both researchers and practitioners.