Application of a reflected forward backward splitting method with momentum to a fractional-order lung cancer model - Izuchukwu, Chinedu; Amilo, David; Sadri, Khadijeh; Yao, Hao-Ren; Yao, Jen-Chih (Communications in nonlinear science & numerical simulation, 2025)
We introduce in this paper, a reflected-forward–backward splitting method that integrates momentum terms to improve the resolution of monotone inclusion problems involving a maximal monotone operator and a monotone Lipschitz continuous operator in a Hilbert space. Momentum terms are integrated to leverage historical information about iterates, thus improving convergence speed. The method that we propose requires one forward computation of the single-valued operator with one backward computation of the set-valued operator per iteration, a key advantage over many existing inertial splitting methods. The practical potential of this method is demonstrated through its application to a fractional-order lung cancer model, where the proposed method showcases its ability to handle complex biological dynamics with improved computational accuracy and reliability. This study makes a significant contribution by demonstrating the method’s versatility in addressing real-world problems involving biological models. •Novel momentum-based reflected-forward–backward splitting for monotone inclusions.•Algorithm applied to fractional-order lung cancer model, capturing complex dynamics.•Algorithm efficient: one forward-backward evaluation, ideal for large problems.•Algorithm effectively captures tumor growth, metastasis, immune dynamics in lung cancer.•Numerical results confirm method handles nonlinear lung cancer dynamics effectively.