Tempered $({\upkappa},\varpi)$-Hilfer Hybrid Pantograph Fractional Boundary Value Problems with Retarded and Advanced Arguments

Abstract

Our research primarily focuses on utilizing tempered $({\upkappa},\varpi)$-fractional operators to explore the existence, uniqueness, and ${\upkappa}$-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.