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1 Journal of Applied Mathematics and Computational Mechanics

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Stability analysis and numerical implementation of the third-order fractional partial differential equation based on the Caputo fractional derivative

Rasheed Sarbast Kamal, Modanli Mahmut, Abdulazeez Sadeq Taha

Journal of Applied Mathematics and Computational Mechanics

2023

Vol. 22, nr 3

33--42

This paper examines a third-order fractional partial differential equation (FPDE) in the Caputo sense. The Theta difference method (TDM) is utilized to investigate the problem, and a first-order difference scheme is developed. Stability estimates are obtained by applying the Von Neumann analysis method. A test problem is presented as an application, and numerical results are obtained using Matlab software. Error estimates, as well as exact and approximate solutions are presented in a data analysis table. The simulation results are shown through error analysis tables and figures.