Coincidence degree theory for higher order nonlinear fractional differential equations: Existence and uniqueness results

Abstract

This paper investigates a new class of fractional differential problems characterized by the ${\rm Y}$-Caputo fractional derivative of order $\varsigma \in (2,3)$. First, the existence result is established via Mawhin’s coincidence degree theory, and subsequently, the uniqueness of solutions is rigorously proved using Banach’s contraction principle. Numerically, the Adomian decomposition method is implemented, providing accurate and efficient approximations. Finally, an illustrative example validates the obtained theoretical results, thereby demonstrating the method’s practical effectiveness and robustness.