In this article, we present extensions of some well-known inequalities such as Young’s inequality and Qi’s inequality on fractional calculus of time scales. To find generalizations of such types of dynamic inequalities, we apply the time scale Riemann-Liouville type fractional integrals. We investigate dynamic inequalities on delta calculus and their symmetric nabla results. The theory of time scales is utilized to combine versions in one comprehensive form. The calculus of time scales unifies and extends some continuous forms and their discrete and quantum inequalities. By applying the calculus of time scales, results can be generated in more general form. This hybrid theory is also extensively practiced on dynamic inequalities.

The theory of multigroups is a generalized group’s theoretic notions in multiset framework. Although myriad of researches have been done in multigroup theory, but some group’s analogue concepts have not been investigated in multigroup setting. In this paper we propose the notions of divisible and pure multigroups and characterize some of their properties. It is established that the image and preimage of homomorphism of divisible and pure multigroups are divisible and pure multigroups. The nexus between divisible and pure multigroups and that of divisible and pure groups are instituted using the concept of cuts of multigroups.

The objective of this paper is to establish a theorem involving a pair of weakly compatible mappings fulfilling a contractive condition of rational type in the context of dislocated quasi metric space. Besides we proved the existence and uniqueness of coupled coincidence and coupled common fixed point for such mappings. This work offers extension as well as considerable improvement of some results in the existing literature. Lastly, an illustrative example is given to validate our newly proved results.

The integrals \(\int_{-\infty}^\infty t_+^{\lambda-1} \phi(t)dt\) and \(\int_0^t(t-s)^{\lambda -1}b(s)ds\) are considered, \(\lambda\neq 0,-1,-2…\), where \(\phi\in C^\infty_0(\mathbb{R})\) and \(0\le b(s)\in L^2_{loc}(\mathbb{R})\). These integrals are defined in this paper for \(\lambda\le 0\), \(\lambda\neq 0,-1,-2,…\), although they diverge classically for \(\lambda\le 0\). Integral equations and inequalities are considered with the kernel \((t-s)^{\lambda -1}_+\).

In this paper we give a new variation of the prime labeling. We call a graph \(G\) with vertex set \(V(G)\) has an odd prime labeling if its vertices can be labeled distinctly from the set \(\big\{1, 3, 5, …,2\big|V(G)\big| -1\big\}\) such that for every edge \(xy\) of \(E(G)\) the labels assigned to the vertices of \(x\) and \(y\) are relatively prime. A graph that admits an odd prime labeling is called an odd prime graph. We give some families of odd prime graphs and give some necessary conditions for a graph to be odd prime. Finally, we conjecture that every prime graph is odd prime graph.

In this study, we define anti complex fuzzy subgroups and normal anti complex fuzzy subgroups under $s$-norms and investigate some of characteristics of them. Later we introduce and study the intersection and composition of them. Next, we define the concept normality between two anti complex fuzzy subgroups by using \(s\)-norms and obtain some properties of them. Finally, we define the image and the inverse image of them under group homomorphisms.

Harvesting has a strong impact on the dynamic evolution of a population subjected to it. In this paper, a fractional-order predator-prey interaction is studied with harvesting affecting both predator and prey populations. Local stability of the coexistence equilibrium point is discussed depending upon the harvesting of prey. Moreover, period-doubling and Neimark-Sacker bifurcations are studied for a wide range of constant harvesting effort of prey.

In this paper, we have established a theorem involving a pair of mappings satisfying a weakly contraction type condition in the context of quasi \(\alpha\)b-metric space and proved the existence and uniqueness of coupled coincidence and coupled common fixed points. The concept of weakly compatibility of the pair of maps is applied to show the uniqueness of coupled common fixed point. This work offers an extension to the published work of Nurwahyu and Aris [1].

In the present paper, we study a differential inequality involving certain differential operator. As a special case of our main result, we obtained certain differential inequalities implying sufficient conditions for meromorphic starlike and meromorphic convex functions of certain order.

In this paper we are interested in the existence of solutions for Navier problem associated with the degenerate nonlinear elliptic equations in the setting of the weighted Sobolev spaces.