New Solutions of Fuzzy-Fractional Fisher Models via Optimal He–Laplace Algorithm

Fuzzy differential equations have gained significant attention in recent years due to their ability model complex systems the presence of uncertainty or imprecise information. These find applications various fields, such as biomathematics, horological processes, production inventory models, epidemic fluid and economic investments. The Fisher is one example, which studies dynamics a population with uncertain growth rates. This study proposes dual parametric extension He–Laplace algorithm for solving time-fractional fuzzy models. proposed methodology uses triangular numbers introduce highly nonlinear fractional under generalized Hukuhara differentiability concept. obtained solutions are validated against existing results crisp form found be more accurate. analyzed by finding different values spatial coordinate ξ , time id="M2"> η id="M3"> ς -cut both upper lower bounds, they presented graphically. analysis reveals that probability density function gradually decreases at left right boundaries when order increased. provides valuable insights into behavior conditions demonstrates effectiveness fuzzy-fractional