An efficient approach for solving a class of fractional anomalous diffusion equation with convergence

• Published in: Physica scripta 2024-07, Vol.99 (7)
• Main Authors: Rashidinia, Jalil, Molavi-Arabshahi, Mahboubeh, Yousefi, Mahnaz
• Format: Article
• Language: English
• Subjects: anomalous diffusion equation; fractional sub-diffusion; Legendre polynomials; nonlinear algebraic system; operational matrix; spectral collocation method
• ISSN: 0031-8949; 1402-4896
• DOI: 10.1088/1402-4896/ad4826

This article presents a study on Fractional Anomalous Diffusion (FAD) and proposes a novel numerical algorithm for solving Cupoto’s type fractional sub-diffusion equations. to convert the fractional model into a set of nonlinear algebraic equations. These equations are efficiently solved using the Levenberg-Marquardt algorithm. The study provides the error analysis to validate the proposed method. The effectiveness and accuracy of the method are demonstrated through several test problems, and its performance and reliability are compared with other existing methods in the literature. The results indicate that the proposed method is a reliable and efficient technique for solving fractional sub-diffusion equations, with better accuracy and computational efficiency than other existing methods. The study’s findings have important implications for researchers working in the field of fractional calculus. They could provide a valuable tool for solving sub-diffusion equations in various applications, including physics, chemistry, biology, and engineering.