Modern Scientific Press

ABSTRACT: The Degree exponent DE matrix of a graph G, denoted by DE(G) whose vertex v_i has degree d_i , is defined as the n × n matrix whose (i, j)-th entry is (d_i)^dj , if v_i and v_j are adjacent and 0 for other cases. The Degree exponent energy (DEE) of G is the sum of absolute values of the eigenvalues of DE of G. In this paper, we present our results on degree exponent polynomial and degree exponent energy of different graph classes.

ABSTRACT: The aim of this work is to study the existence of solutions for a new class of hybrid Hilfer fractional differential with boundary hybrid conditions. To prove the main results, we use a hybrid fixed point theorem for the sum of three operators due to Dhage. An example illustrating the main result is also constructed.

ABSTRACT: Wavelet analysis is newly developed mathematical tool and have been applied extensively in many engineering fields. Wavelets are used as tools that cut functions or operators into different frequency components, and then study each component with a resolution matching to its scale. In this paper, we proposed the numerical solution of nonlinear partial differential equations by Biorthogonal wavelet based full approximation scheme. The proposed method gives higher accuracy in terms of better convergence with low computational time, which has been demonstrated through some test problems.

ABSTRACT: This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using new Homotopy analysis method. In this paper, a non-linear mathematical model is used to analyse the dynamical relationship between predator and their prey. This paper presents an approximate analytical method to solve the non-linear differential equations. A simple and closed form of analytical expressions for three dimensional Lotka – Volterra model are obtained. Numerical simulations are carried out to justify analytical results.