Direct consequences of the form of Gröbner–Shirshov basis for the monoid of positive braids are given: canonical forms for positive braids and square-free braids, computation of the exponent of a positive braid, of the initial set and of the longest initial route, divisibility properties and other related results.
In this article, we aim to prove various unique fixed point results for contractive and weakly compatible mappings in the sense of neutrosophic metric spaces. Several nontrivial examples are also imparted. To support main result, uniqueness of solution of nonlinear fractional differential equations is examined.
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