aspg-21-581-1791468618 20261008141018 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2020 10 1 Muhammad Naveed Jafar Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan Ezgi TÜRKARSLAN Department of Mathematics, TED University, Ön Cebeci, Ziya Gökalp Cd. 48/A, 06420 Çankaya/Ankara, Turkey Ali Hamza Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan Sara Farooq Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan The concept of neutrosophic become really handy now a days and based on non-standard analysis to mention mathematical outcomes, uncertainty, non-completed situations, inconsistency, distinctness. The main concept of Neutrosophic set based on membership values of truth, indeterminacy and falsity, which are independent, and which play vital role in situations like uncertainty, incomplete and inconsistence. From triangular to octagonal Neutrosophic number. They play vital role in modeling problems, science, biology and many more. Hence it is clear that these are necessary and have real life applications, but some real-life problems have more edges and their triangular to octagonal fail to overcome this situation (mention in table 1). Hence, nonagonal neutrosophic numbers give a wide scope of utilizations while managing more variances in the decision-making condition with nine edges for membership values of truth, indeterminacy and falsity. In this current article we present compression between triangular to nonagonal neutrosophic number and their requirement, explore differential equations in Neutrosophic environment as Linear, symmetric and asymmetric types further, their ∂-cute and then we present a real-life problem and solved it with TOPSIS technique of MCDM. 2020 45 64 581 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.0100104 https://www.americaspg.com/journal/21/article/581 https://www.americaspg.com/storage/7751.pdf