In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.

In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.

The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

The beet armyworm (BAW), Spodoptera exigua (Lepidoptera: Noctuidae) is a highly destructive pest of vegetables and field crops. Management of beet armyworm primarily relies on synthetic pesticides, which is threatening the beneficial community and environment. Most importantly, the BAW developed resistance to synthetic pesticides with making it difficult to manage. Therefore, alternative and environment-friendly pest management tactics are urgently required. The use of pesticidal plant extracts provides an effective way for a sustainable pest management program. To evaluate the use of pesticidal plant extracts against BAW, we selected six plant species (Lantana camara, Aloe vera, Azadirachta indica, Cymbopogon citratus, Nicotiana tabacum ,