Journal of Applied Science and Engineering

Published by Tamkang University Press

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Efficient Caputo-based Solutions for Linear Time-Fractional Partial Differential Equations in Two and Three Dimensions

 2026

 Volume 32

Iman I. Gorial1,2 and Luma N. M. Tawfiq1

1Department of. Mathematics /College of Education for Pure Science (Ibn Al-Haitham)/ University of Baghdad

2Department of General Material Engineering/College of Materials Engineering/ University of Technology

Received: January 3, 2026
Accepted: April 26, 2026
Publication Date: May 27, 2026

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Accuracy of the results, for example 1, σ = ω = 0.3 

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This study presents a new and highly efficient method for solving linear time-fractional partial differential equations (TFPDEs) in two and three dimensions. The proposed method utilizes Caputo fractional derivative to represent the time derivatives. The efficiency of this method is shown by four examples: two-dimensional fractional parabolic equation, three-dimensional fractional diffusion equation, two-dimensional fractional equations, and a three-dimensional fractional heat equation. The outcomes of this study indicate that the proposed method offers accurate and efficient analytical solutions with very simple implementation steps. Therefore, it is suitable to solve a great variety of models in engineering, physics and other scientific fields involving fractional partial differential equations.

Keywords: Riemann-Liouville fractional integral operator, Caputo derivatives, Mittage Leffler function, Fractional parabolic equation, Fractional diffusion equation, Fractional heat equation.

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