Faisal Yousafzai

On Intra-Regular Left Almost Semihypergroups with Pure Left Identity

We characterize intra-regular LA-semihypergroups by using the properties of their left and right hyperideals, and we investigate some useful conditions for an LA-semihypergroup to become an intra-regular LA-semihypergroup.

On fuzzy fully regular ordered

We have introduced and characterized a fully regular (V-regular) class of an ordered AG-groupoid in terms of fuzzy (left, right, two-sided, interior, bi-, generalized biand quasi) ideals. We have shown that all these fuzzy ideals need not to be coincide in an ordered AG-groupoid S even if S has a left identity but on the other hand, it has been shown that all these fuzzy ideals coincide in a V-regular ordered AG-groupoid with a left identity.

\mathcal{AG}

In this work, we consider giving up smoking dynamic on adolescent nicotine dependence. First, we use the Caputo derivative to develop the model in fractional order. Then we apply two different numerical methods to compute accurate approximate solutions of this new model in fractional order and compare their results. In order to do this, we consider the generalized Euler method (GEM) and multi-step generalized differential transform method (MSGDTM). We also show the unique positive solution for this model and present numerical results graphically.

-groupoids

We generalize the idea of (, )-fuzzy ordered semi-group and give the concept of (, )-fuzzy ordered -semigroup. We show that (, )-fuzzy left (right, two-sided) ideals, (, )-fuzzy (generalized) bi-ideals, (, )-fuzzy interior ideals and (, )-fuzzy (1, 2)-ideals need not to be coincide in an ordered -semigroup but on the other hand, we prove that all these (, )-fuzzy ideals coincide in a left regular class of an ordered -semigroup. Further we investigate some useful conditions for an ordered -semigroup to become a left regular ordered -semigroup and characterize a left regular ordered -semigroup in terms of (, )-fuzzy one-sided ideals. Finally we connect an ideal theory with an (, )-fuzzy ideal theory by using the notions of duo and ()-fuzzy duo.

Approximating a Giving Up Smoking Dynamic on Adolescent Nicotine Dependence in Fractional Order.

An ordered AG-groupoid can be referred to as an ordered left almost semigroup, as the main difference between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an ordered AG-groupoid and use them to characterize a strongly regular class of a unitary ordered AG-groupoid along with its semilattices and fuzzy one-sided ideals. We also introduce the concept of an ordered -groupoid and investigate its structural properties by using the generated ideals and fuzzy one-sided ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.

(∈, ∈ ∨q k )-FUZZY IDEALS IN LEFT REGULAR ORDERED

[This corrects the article DOI: 10.1371/journal.pone.0103617.].