In this paper, we are concerned with the existence and uniqueness of global strong solution of non-planar oscillations for a nonlinear coupled Kirchhoff beam equations with moving boundary.

Graph labeling plays an important role in different branches of sciences. It gives useable information in the study of radar, missile and rocket theory. In scheme theory, coding theory and computer networking graph labeling is widely employed. In the present paper, we find necessary conditions for the octagonal planner map and multiple wheel graph to be super cyclic antimagic cover and then discuss their super cyclic antimagic covering.

The double dispersive wave equation with memory and source terms \(u_{tt}-\Delta u-\Delta u_{tt}+\Delta^{2}u-\int_{0}^{t}g(t-\tau)\Delta^{2}u(\tau)d\tau-\Delta u_{t}=|u|^{p-2}u\) is considered in bounded domain. The existence of global solutions and decay rates of the energy are proved.

This paper presents the development of a new numerical scheme for the solution of exponential growth and decay models emanated from biological sciences. The scheme has been derived via the combination of two interpolants namely, polynomial and exponential functions. The analysis of the local truncation error of the derived scheme is investigated by means of the Taylor’s series expansion. In order to test the performance of the scheme in terms of accuracy in the context of the exact solution, four biological models were solved numerically. The absolute error has been computed successfully at each mesh point of the integration interval under consideration. The numerical results generated via the scheme agree with the exact solution and with the fifth order convergence based upon the analysis carried out. Hence, the scheme is found to be of order five, accurate and is a good approach to be included in the class of linear explicit numerical methods for the solution of initial value problems in ordinary differential equations.

A new series representation of the modified Bessel function of the second kind \(K_0(x)\) in terms of simple elementary functions (Kummer’s function) is obtained. The accuracy of different orders in this expansion is analysed and has been shown not to be so good as those of different approximations found in the literature. In the sequel, new polynomial approximations for \(K_0(x)\), in the limits \(0<x\leq 2\) and \(2\leq x < \infty\), are obtained. They are shown to be much more accurate than the two best classical approximations given by the Abramowitz and Stegun’s Handbook, for those intervals.

The aim of this paper is to study the fractional Hadamard inequalities for Caputo fractional derivatives of strongly convex functions. We obtain refinements of two known fractional versions of the Hadamard inequality for convex functions. By applying identities for Caputo fractional derivatives we get refinements of error bounds of these inequalities. The given results simultaneously provide refinements as well as generalizations of already known inequalities.

The recently introduced class of vertex-degree-based molecular structure descriptors, called Sombor indices (\(SO\)), are examined and a few of their basic properties established. Simple lower and upper bounds for \(SO\) are determined. It is shown that any vertex–degree–based descriptor can be viewed as a special case of a Sombor-type index.

This paper considers the extension of the Adomian decomposition method (ADM) for solving nonlinear ordinary differential equations of constant coefficients to those equations with variable coefficients. The total derivatives of the nonlinear functions involved in the problem considered were derived in order to obtain the Adomian polynomials for the problems. Numerical experiments show that Adomian decomposition method can be extended as alternative way for finding numerical solutions to ordinary differential equations of variable coefficients. Furthermore, the method is easy with no assumption and it produces accurate results when compared with other methods in literature.

In this paper, we introduce a new class of analytic functions by using the lambda operator and obtain some subordination results.

In this paper, we introduce the notion of modified Suzuki-Edelstein-Geraghty proximal contraction and prove the existence and uniqueness of best proximity point for such mappings. Our results extend and unify many existing results in the literature. We draw corollaries and give illustrative example to demonstrate the validity of our result.