In this paper, a novel spectral collocation method using Legendre multi-wavelets as the basis functions is presented to obtain the numerical solution of nonlinear fractional differential equations. The fractional derivative is described in the Caputo sense. The two-scale relations of Legendre multi-wavelets and the properties of block pulse functions have been used in the evaluation of the fractional integral operational matrix and expansion coefficients of the nonlinear terms for the Legendre multi-wavelets. Due to the aforementioned properties, the original differential equation is converted into a nonlinear system of algebraic equations which can be solved by existing tools. The numerical results are compared with exact solutions and existing numerical solutions found in the literature and demonstrate the validity and applicability of the proposed method.
This paper describes a study using Average Monthly Exchange Rates (AMER) of Naira (Nigerian currency) to six other currencies of the World to evaluate and compare the performance of univariate and multivariate based time series models. The data from 2002 -2014 was used for modeling and forecasting the actual values of the AMER for 2014 of the six currencies. The Mean Absolute Percentage Error (MAPE) forecast accuracy measure was also used in determining if Univariate Times Series Model or Multivariate Time Series Models is best for forecasting the future AMER value of a given currency. The result of data showed that the Univariate time series fits better for Dollar, Pounds Sterling, Yen, WAUA and CFA, while only Euro fits well for the Multivariate time series.
In the present paper, a traveling wave solution has been established using the modified extended tanh method for space-time fractional nonlinear partial differential equations. We used this method to find exact solutions for different types of the space-time fractional nonlinear partial differential equations such as space-time fractional regularized long wave equation (RLWE) and space-time fractional modified regularized long wave equation (MRLW) which are the important soliton equations. Both equations are reduced to ordinary differential equations by using of fractional complex transform and properties of modified Riemann-Liouville derivative.
In this work, we propose an HIV infection model with cure of infected cells in eclipse stage and delay in the activation of immune response. The stability of the equilibria and the existence of the Hopf bifurcation are investigated. Moreover, numerical simulations are carried out to illustrate our theoretical results.
In this paper, we define the concepts of (F, L)-contraction and (F,L)-weak contraction in weak partial metric space which is generalized metric space. Using these concepts we prove some common fixed point theorems for two self mappings and we give some fixed point results for a single mapping in weak partial metric spaces. Also, we give some examples to support our new results. The theorems obtained here extend and generalize many results in the literature.
