International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3825 2020 2020 School of Mathematical Sciences, University Sains Malaysia, 11800 Penang, Malaysia Abdulsalam Abdulsalam School of Mathematical Sciences, University Sains Malaysia, 11800 Penang, Malaysia Amirah Azmi Tikrit university, College of Education for Pure Science, Tikrit, Iraq Yaseen S.. R. Applying Chebyshev polynomial approximate results, this paper applies the idea of neutrophilic logic to the approach to partially differential equations (FPDEs).  Three elements make up the Neutrosophic technique: Indeterminacy (I), Falsehood (F), and Truth (T).  These three elements are appropriate for issues where precise values or distinct limits are lacking since they are utilized to represent ambiguity, vagueness, and imperfect truth in mathematical models.  We improve the depiction of real-world occurrences that could contain unclear or ambiguous information by adding these values to the coefficients of FPDEs.  In domains like material science, mechanical engineering, and biological phenomena, where uncertainty is inevitable, the use of neutrophilic logic enables a more thorough and precise approximation of approaches to complicated fractional differential equations. The findings show that when working with systems that have unknown characteristics, the Neutrosophic technique increases the accuracy and dependability of computations. 2025 2025 339 358 10.54216/IJNS.260325 https://www.americaspg.com/articleinfo/21/show/3825