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.

ABSTRACT: The spread of Coronavirus (Covid-19) cases has been alarming all over the World. On the 15 June, 2020 in Nigeria, there were 576 Confirmed Corona virus cases 10,885 active cases, 16,658 cumulative (Covid-19) cases and 424 total deaths. These data have been analyzed recently using the linear regression models and various curve models with less accurate results and poor forecast performance. Data were collected from the Worldometer website that provides updates on Coronavirus statistics around the World. Based on the time structured nature of Covid-19 cases that evolve stochastically, this paper therefore aimed at modeling Covid-19 variables using ARIMA(p,d,q) model with a view to forecasting daily, cumulative confirmed cases, number of active cases and death cases for the months of December, 2020 and January, 2021. The forecast values were found to be increasing, and very close to the actual values for the out-sample cases with minimum mean square forecast errors.

ABSTRACT: A general linear-type time series imitation namely Autoregressive Integrated Moving Average (ARIMA) models have played indispensable theoretical and practical role in the representation and analysis of time series data. These theoretical and practical representations are usually denoted by ARIMA (p, d, q). When d, the differencing operator (integrating parameter) is zero the resulting models are also a generalize type called Autoregressive Moving Average Models (ARMA). It is of great importance to review members of the family of ARIMA because seeing these members at a glance will bring a better understanding and correct application of these models to time series data. Thirteen members of the family of ARIMA were reviewed in the presence of autocorrelation function.