2024/10/26 by Deeksha Singh, Singh, Deeksha, Swati Yadav +3
Mathematics · #35R11 #65M06 #65M12 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2410.20192
openalex publication_date 2024/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a numerical method to solve a time-fractional Burgers equation, achieving order of convergence (2-α) in time, here α represents the order of the time derivative. The fractional derivative is modeled by Caputo-Prabhakar (CP) formulation, which incorporates a kernel defined by the three-parameter Mittag-Leffler function. Finite difference methods are employed for the discretization of the derivatives. To handle the non-linear term, the Newton iteration method is used. The proposed numerical scheme is proven to be stable and convergent in the L∞ norm. The validity of the theory is supported by two numerical examples.