aspg-21-2896-1791475928 20261008161208 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 4 Mohammed Qassim College of the Basic Education, Mathematics and Computer Department, University of Babylon, Iraq Mohammed Abed Daim Zoba College of the Basic Education, Mathematics and Computer Department, University of Babylon, Iraq Ahmed Hadi Hussain College of the Engineering, Al-Musayab, Energy Engineering Department, University of Babylon In this work, fractional partial equations' and neutrosophic fractional partial equations analytical series solutions are presented, we consider the fractional derivative in the meaning of Caputo in these formulas. We offer a novel objective method the LRPS which is a strong instrument for precise analytically and numerical solutions to these problems by setting an excellent example, we stress precision, effectiveness, and application style, also we can find exact answers when there is a pattern between the series' parts; alternatively, we can only offer approximations. The Mathematica application is used to assess the numerical and graphical findings to make sure the solutions generated are accurate and that the approach can be modified to solve this kind of this problem. The findings obtained demonstrated that our current procedure is appropriate and efficient for resolving PDEs. 2024 257 267 2896 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240419 https://www.americaspg.com/journal/21/article/2896 https://www.americaspg.com/storage/21718591484.pdf