A Novel Romanovski-Jacobi Spectral Collocation Scheme for Fourth-Order ψ Fractional Sub-Diffusion Models

Abstract

This paper presents a novel Romanovski-Jacobi (R-J) spectral collocation scheme for numerically solving Fourth-Order ψ-Fractional Sub-Diffusion models (FO-ψFSDEs). These models, which are governed by ψ-fractional differential equations, play a crucial role in accurately capturing memory and hereditary properties in complex anomalous diffusion phenomena, particularly in physics and biology. Due to the analytical complexity of such equations, the development of efficient numerical methods is essential. The proposed R-J Spectral Collocation (RJSC) approach leverages the orthogonality and localization properties of R-J polynomials to construct highly accurate approximations. The study demonstrates the robustness and precision of the method through several benchmark examples, emphasizing its potential for modeling and simulating real-world fractional dynamical systems.