Novel Investigation of Hepatitis B Transmission Dynamics via Fractal-Fractional Operators of Variable and Constant Order with Memory Effects

A fractional-order (hepatitis B virus) HBV transmission model is developed using Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo (ABC) operators to capture memory effects and non-local interactions-including asymptomatic carriers and vertical transmission. Existence, uniqueness, positivity, and stability of solutions are established via fixedpoint theorems and Ulam-Hyers criteria. Numerical simulations employ Adams-Bashforth-Moulton and predictor-corrector methods adapted to each fractional derivative. Results show that lowering the fractional order (α < 1) reduces peak viral load, especially with early intervention, but extends infection duration due to slower decay. This fractional modelling framework offers deeper insight into chronic HBV dynamics, vaccination effectiveness, and long-term control strategies.