Application of a reflected forward backward splitting method with momentum to a fractional-order lung cancer model

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 le...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation Vol. 151; p. 109055
Main Authors: Izuchukwu, Chinedu, Amilo, David, Sadri, Khadijeh, Yao, Hao-Ren, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2025
Subjects:
Fractional-order model
Lung cancer
Momentum term
Monotone inclusion
Monotone operators
Reflected-forward–backward method
47H10
Reflected-forward–backward method
Monotone inclusion
49J20
Monotone operators
49J40
Lung cancer
Fractional-order model
47H09
Momentum term
ISSN:1007-5704
Online Access:Get full text
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Summary: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.
ISSN:1007-5704
DOI:10.1016/j.cnsns.2025.109055