Existence results and stability analysis for a fractional spatiotemporal brain tumor and immune system interaction
European Physical Journal Plus, vol.141, no.5, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 141 Issue: 5
- Publication Date: 2026
- Doi Number: 10.1140/epjp/s13360-026-07747-w
- Journal Name: European Physical Journal Plus
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: 35R11, 37N25
- Karadeniz Technical University Affiliated: No
Abstract
In this paper, we present an innovative model that provides a comprehensive framework for understanding the complex interactions between glioma cells and immune cells in the progression of brain cancer. This study stands out by addressing the limitations of traditional diffusion models, which often fall short in capturing the irregular and non-local movements of cells within the tumor microenvironment. To overcome these challenges, we employ fractional time derivatives and the fractional Laplacian operator, offering a more accurate depiction of the anomalous diffusion processes crucial to cancer dynamics. Our research begins with a rigorous mathematical analysis, establishing the global existence of a unique mild solution, thereby providing a solid theoretical foundation for the model. A key contribution of our study is the introduction of the “invasion threshold,” a critical parameter inspired by the next-generation operator from epidemiological modeling. This threshold serves as a powerful tool for determining the existence and stability of equilibrium points, offering valuable insights into the conditions that either promote or inhibit tumor growth.