A hybrid numerical framework for solving high dimensional p−Laplacian type fractional systems with Caputo-Katugampola derivatives via GL1−2 discretization and grey wolf optimization
Computers and Mathematics with Applications, cilt.221, ss.1-15, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 221
- Basım Tarihi: 2026
- Doi Numarası: 10.1016/j.camwa.2026.07.023
- Dergi Adı: Computers and Mathematics with Applications
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Applied Science & Technology Source, Compendex, INSPEC, MathSciNet, MLA - Modern Language Association Database, zbMATH, MLA International Bibliography, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Sayfa Sayıları: ss.1-15
- Anahtar Kelimeler: Caputo-Katugampola derivative, Fractional differential equations, GL1−2 Discretization, Grey wolf optimization, Memory dependent systems, P-Laplacian operator
- İstanbul Ticaret Üniversitesi Adresli: Hayır
Özet
Fractional differential equations (FDEs) provide a rigorous framework for modeling complex dynamical systems with memory and hereditary effects, arising in viscoelasticity, control theory, bioengineering, finance, and neural dynamics. Yet, solving nonlinear infinite-dimensional systems involving the Caputo–Katugampola derivative and the p -Laplacian operator in tempered sequence spaces ℓpα remains highly challenging due to strong memory effects, nonlocality, and nonlinear coupling. This work introduces a hybrid numerical framework that integrates the generalized GL1−−2 discretization scheme with the Grey Wolf Optimization (GWO) algorithm to approximate solutions of infinite-dimensional p -Laplacian type FDEs. The GL1−−2 scheme employs a nonlinear transformation s ↦ sμ to construct a refined non-uniform grid, enhancing accuracy for small fractional orders while preserving memory effects. The resulting nonlinear residual system is reformulated as an optimization problem and handled through GWO, a derivative-free metaheuristic inspired by the social hierarchy and hunting strategy of grey wolves. Numerical experiments and sensitivity analyses demonstrate the stability, residual-reduction capability, and robustness of the proposed method under the considered fractional parameter settings. In contrast to existence-only results in the literature, typically formulated under the theoretical condition M < 1, the present framework constructively computes explicit numerical approximations. Residual-based validation further confirms stable and consistent convergence behavior across the tested configurations. The integration of GL1−−2 and GWO provides a robust mechanism for handling nondifferentiable and memory-dependent systems, offering a versatile computational tool that can be extended to variable-order models, multi-dimensional domains, and stochastic fractional systems.