Tempered (κ, ϖ)-Hilfer hybrid pantograph fractional boundary value problems with retarded and advanced arguments

Our research primarily focuses on utilizing tempered (?, ?)-fractional operators to explore the existence, uniqueness, and ?-Mittag-Leffler-Ulam-Hyers stability of a specific class of hybrid Pantograph boundary value problems involving both retarded and advanced arguments. Our approach is based on Banach?s fixed-point theorem, along with a generalized form of the well-known Gronwall inequality. Furthermore, we include an illustrative example to demonstrate the practical implications of our findings.