Existence and Uniqueness Theorems for a Variable-Order Fractional Differential Equation with Delay

This study establishes the existence and stability of solutions for a general class Riemann–Liouville (RL) fractional differential equations (FDEs) with variable order finite delay. Our findings are confirmed by fixed-point theorems (FPTs) from available literature. We transform RL FDE to alternate integral structure, then use classical FPTs, results studied Hyers–Ulam is established help standard notions. The approach more broad-based same methodology can be used number additional issues.