{"id":7370,"date":"2026-05-27T18:41:10","date_gmt":"2026-05-27T10:41:10","guid":{"rendered":"\/jase\/?post_type=tkuisotope&p=7370"},"modified":"2026-05-27T20:25:08","modified_gmt":"2026-05-27T12:25:08","slug":"jase-202609-32-055","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=jase-202609-32-055","title":{"rendered":"Efficient Caputo-based Solutions for Linear Time-Fractional Partial Differential Equations in Two and Three Dimensions"},"content":{"rendered":"\n
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<\/i> 2026<\/a><\/p>\n<\/div>\n\n\n\n

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<\/i> Volume 32<\/a><\/p>\n<\/div>\n\n\n\n

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Iman I. Gorial1,2<\/sup><\/i><\/a> and Luma N. M. Tawfiq1<\/sup><\/p>\n\n\n\n

1<\/sup>Department of. Mathematics \/College of Education for Pure Science (Ibn Al-Haitham)\/ University of Baghdad<\/p>\n\n\n\n

2<\/sup>Department of General Material Engineering\/College of Materials Engineering\/ University of Technology<\/p>\n<\/div>\n\n\n\n

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Received: January 3, 2026
Accepted: April 26, 2026
Publication Date: May 27, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n

\"\u4e0a\u50b3\u5716\u7247\"\n\n\n

Accuracy of the results, for example 1, \u03c3 = \u03c9 = 0.3 <\/p>\n<\/div>\n<\/div>\n\n\n\n

<\/i> Copyright <\/strong>The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n

Download Citation:\u00a0 BibTeX <\/a>| http:\/\/dx.doi.org\/10.6180\/jase.202609_32.055<\/a>\u00a0\u00a0<\/p>\n\n\n\n

Download PDF<\/a><\/p>\n\n\n\n

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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.<\/p>\n\n\n\n

Keywords: Riemann-Liouville fractional integral operator, Caputo derivatives, Mittage Leffler function, Fractional parabolic equation, Fractional diffusion equation, Fractional heat equation.<\/em><\/p>\n\n\n\n

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