Journal of Education for Pure Science-University of Thi-Qar

In this paper, we study neutrosophic hesitant fuzzy ideal. We introduce the notions of neutrosophic
hesitant fuzzy primary ideal, neutrosophic hesitant fuzzy semiprimary ideal of a ring and discussion of
some important theorems and results.

The homotopypermutation approach is used in this article to solve the fractional-order biological population model (FOBPM). The fractional derivative is defined using the Atangana-Baleanu operator (ABO). The suggested technique provides of several solutions for FOBPM. The HPM technique is regarded as one of the finest analytical processes for solving fractional-order, nonlinear PDEs, notably the FOBPM, Since it requires fewer computations and has a greater rate of convergence than other analytical approaches.