A High-Precision Hybrid Semi-Analytical Technique for Solving Fractional Reaction-Diffusion Models
Keywords:
Tantawy Least Squares Method, Allen-Cahn Equation, Newell-Whitehead Equation, Fisher's Equation, Caputo Derivative, Fractional Reaction-Diffusion EquationsAbstract
In this work, we solve a class of nonlinear time-fractional reaction-diffusion equations using the Tantawy Least Squares Method (TLSM), a high-precision hybrid semi-analytical technique. In particular, we study the fractional Allen-Cahn, Newell-Whitehead, and Fisher's equations, which are essential for simulating fluid convection patterns, population genetics, and phase separation. The TLSM offers a clear benefit over conventional variational and perturbation methods by combining the Tantawy technique's iterative power series structure with a least-squares residual error minimization. For these models, we obtain the general recurrence relations under the Caputo fractional derivative operator. Thorough residual error analysis is used to validate the accuracy of the suggested approach. In terms of convergence speed and absolute error, comparative numerical studies show that TLSM performs noticeably better than the Modified Variational Iteration Algorithm-II.
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Copyright (c) 2026 Harun Çiçek, Zulqurnain Sabir, Fevzi Erdoğan, Nadeem Rao (Author)
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