In this paper, we establish viscosity rule for common fixed points of two nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this work extend and improve some recent announced in the literature.

In this work, we developed homotopy perturbation double Sumudu transform method (HPDSTM) which is obtained by combining homotopy perturbation method, double Sumudu transform and He’s polynomials. The method is applied to find the solution of linear fractional one and two dimensional dispersive KdV and nonlinear fractional KdV equations to illustrate the reliability of the method. It is observed that the solutions obtained by the method converge rapidly to the exact solutions. This method is very powerful, and professional techniques for solving different kinds of linear and nonlinear fractional order differential equations.

In this article, we compute closed forms of M-polynomial for three general classes of convex polytopes. From the M-polynomial, we derive degree-based topological indices such as first and second Zagreb indices, modified second Zagreb index, Symmetric division index, etc.

Let \(G\) be a simple connected molecular graph with vertex set \(V(G)\) and edge set \(E(G)\). One important modification of classical Zagreb index, called hyper Zagreb index \(HM(G)\) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms \({[{{d}_{G}}(u)+{{d}_{G}}(v)]^2}\) over all the edges of \(G\), where \(d_G(v)\) denote the degree of the vertex \(u\) of \(G\). In this paper, the hyper Zagreb index of certain bridge and chain graphs are computed and hence using the derived results we compute the hyper Zagreb index of several classes of chemical graphs and nanostructures.

Chemical reaction network theory is an area of applied mathematics that attempts to model the behavior of real world chemical systems. Since its foundation in the 1960s, it has attracted a growing research community, mainly due to its applications in biochemistry and theoretical chemistry. It has also attracted interest from pure mathematicians due to the interesting problems that arise from the mathematical structures involved. It is experimentally proved that many properties of the chemical compounds and their topological indices are correlated. In this report, we compute closed form of forgotten polynomial and forgotten index for interconnection networks. Moreover we give graphs to see dependence of our results on the parameters of structures.

In this paper, we present a new viscosity technique of nonexpansive mappings in the framework of CAT(0) spaces. The strong convergence theorems of the proposed technique is proved under certain assumptions imposed on the sequence of parameters. The results presented in this paper extend and improve some recent announced in the current literature.