Open Journal of Mathematical Sciences (OMS)

Some new inequalities of Simpson’s type for functions whose third derivatives in absolute value at some powers are strongly \((s,m)\)- convex in the second sense are provided. An application to the Simpson’s quadrature rule is also provided.

This paper investigates the squeezing flow of an electrically conducting magnetohydrodynamic Casson nanofluid between two parallel plates embedded in a porous medium using differential transformation and variation of parameter methods. The accuracies of the approximate analytical methods for the small and large values of squeezing and separation numbers are investigated and established. Good agreements are established between the results of the approximate analytical methods are compared with the results numerical method using fourth-fifth order Runge-KuttaFehlberg method. However, the results of variation of parameter methods show better agreement with the results of numerical method than the results of differential transformation method. Thereafter, the developed approximate analytical solutions are used to investigate the effects of pertinent flow parameters on the squeezing phenomena of the nanofluids between the two moving parallel plates. The results established that the squeezing number and magnetic field parameters decrease as the flow velocity increases when the plates were coming together. Also, the velocity of the nanofluids further decreases as the magnetic field parameter increases when the plates move apart. However, the velocity is found to be directly proportional to the nanoparticle concentration during the squeezing flow i.e. when the plates are coming together and an inverse variation between the velocity and nanoparticle concentration is recorded when the plates are moving apart. As increased physical insights into the flow phenomena are provided, it is hope that this study will enhance the understanding the phenomena of squeezing flow in various applications such as power transmission, polymer processing and hydraulic lifts.

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.