Analysis of the Existence and Stability of Solutions for a Class of Four-Term Fractional Differential Equations

This study investigates a category of high-order sequential fractional boundary value problems involving four-term fractional derivatives. Motivated by the nonlocal properties of fractional calculus and the limitations of available models with fewer derivatives, the solutions of a novel four-term sequential fractional differential equation under hybrid boundary conditions are researched regarding whether they are unique and satisfy the stability of Ulam–Hyers. To leverage Banach’s contraction principle (CP) and Krasnoselskii’s fixed-point theorem (FPT), rigorous existence criteria are constructed, and a computable Ulam–Hyers stability constant is derived. A key innovation lies in addressing the analytical challenges posed by multiple fractional operators through operator decomposition and integral inequality techniques. A numerical example validates the theoretical framework, demonstrating the applicability of the proposed methods. The results extend prior work on two terms and provide a foundation for modeling complex systems with higher-order memory effects.