Open Journal of mathematical Sciences (OMS)

In the field of computer networks, the performance of data transmission is usually characterized by the fractional factor. Some sufficient conditions for the existence of Hamilton fractional factors are obtained in this paper, and they extend the original theory presented in Gao et al. [1].

In this paper we are concerned with the problem of asymptotic integration of positive solutions of higher order fractional differential equations with Caputo-type Hadamard derivative of the form \(^{C,H}D_{a}^r x(t)=e(t)+f(t,x(t)), \; a>1,\) where \(r = n +\alpha -1, \alpha\in (0, 1), n \in \mathbb{Z}^+\). We shall apply our technique to investigate the oscillatory and asymptotic behavior of all solutions of the integral equation \(x(t)=e(t)+\int_a ^t (\ln\frac{t}{s} )^{r-1} k(t,s)f(s,x(s))\frac{ds}{s}, \; a>1,\) \(r\) is as above.

We present a compartmental mathematical model of (SITR) to investigate the effect of saturation treatment in the dynamical spread of diarrhea in the community. The mathematical analysis shows that the disease free and the endemic equilibrium points of the model exist. The disease-free equilibrium is locally and globally asymptotically stable when \(R_{0}<1\) and unstable otherwise \(R_{0}>1\). Numerical simulation results, show the effect of saturation treatment function on the spread of diarrhea. Efficacy of treatment shows a great impact in the total eradication of diarrhea epidemic.

In this paper, we find the general solution of a Septoicosic functional equation (11) for all \(x, y \in X\) and investigate its general Hyers-Ulam stability in Banach Space using direct and fixed point methods.

In this paper, we study Katugampola fractional differential equations (FDEs) with nonlocal conditions on time scales. By means of standard fixed point theorems, some new sufficient conditions for the existence of solutions are established.

The objective of this paper is to study new type of continuous functions called totally \(\alpha\) gs-continuous functions using \(\alpha\) gs-open sets. Furthermore we discuss covering properties and obtain their characterizations by including counter examples.

A simple graph \(G=(V(G),E(G))\) admits an \(H\)-covering if \(\forall \ e \in E(G)\ \Rightarrow\ e \in E(H’)\) for some \((H’ \cong H )\subseteq G\). A graph \(G\) with \(H\) covering is an \((a,d)\)-\(H\)-antimagic if for bijection \(f:V\cup E \to \{1,2,\dots, |V(G)|+|E(G)| \}\), the sum of labels of all the edges and vertices belong to \(H’\) constitute an arithmetic progression \(\{a, a+d, \dots, a+(t-1)d\}\), where \(t\) is the number of subgraphs \(H’\). For \(f(V)= \{ 1,2,3,\dots,|V(G)|\}\), the graph \(G\) is said to be super \((a,d)\)-\(H\)-antimagic and for \(d=0\) it is called  \(H\)-supermagic. In this paper, we investigate the existence of super \((a,d)\)-\(C_3\)-antimagic labeling of a corona graph, for differences \(d=0,1,\dots, 5\).

In this paper, we use the Delta Riemann-Liouville fractional integrals to establish some new integral inequalities for the Chebyshev functional in the case of two synchronous functions on time scales. Our results improve the inequalities for the discrete and continuous cases.

Let \(k>0\) an integer. \(F\), \(\tau \), \(N\), \(N_{k}\), \(N_{k}^{(2)}\) and \(A\) denote the classes of finite, torsion, nilpotent, nilpotent of class at most \(k\), group which every two generator subgroup is \(N_{k}\) and abelian groups respectively. The main results of this paper is, firstly, we prove that, in the class of finitely generated \(\tau N\)-group (respectively \(FN\)-group) a \((FC)\tau \)-group (respectively \((FC)F\)-group) is a \(\tau A\)-group (respectively is \(FA\)-group). Secondly, we prove that a finitely generated \(\tau N\)-group (respectively \(FN\)-group) in the class \(((\tau N_{k})\tau ,\infty)\) (respectively \(((FN_{k})F,\infty)\)) is a \(\tau N_{k}^{(2)}\)-group (respectively \(FN_{k}^{(2)}\)-group). Thirdly we prove that a finitely generated \(\tau N\)-group ( respectively \(FN\)-group) in the class \(((\tau N_{k})\tau ,\infty)^{\ast}\) (respectively \(((FN_{k})F,\infty)^{\ast}\)) is a \(\tau N_{c}\)-group (respectively \(FN_{c}\)-group) for certain integer \(c\) and we extend this results to the class of \(NF\)-groups.

The generalized hierarchical product of graphs was introduced by L. Barrière et al. in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs are obtained. Finally using the derived results the reformulated first Zagreb index of some chemically important graphs such as square comb lattice, hexagonal chain, molecular graph of truncated cube, dimer fullerene, zig-zag polyhex nanotube and dicentric dendrimers are computed.