in this paper, we apply the differential transform (dt) method for finding approximate solution of the system of linear and nonlinear volterra integro-differential equations with variable coefficients, especially of higher order. we also obtain an error bound for the approximate solution. since, in this method the coefficients of taylor series expansion of solution is obtained by a recurrence r...

In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

In this study, Lane–Emden complex differential equations have been randomized by selecting random variables for the coefficients, initial conditions, and force functions of equations. addition, finding solutions obtained equations, probability characteristics are examined. The version transformation method (DTM) is used to obtain an analytical solution close equation. Approximate expected value...

In dynamics, the Van der Pol oscillator is a non-conservative with non-linear damping. The problems of single-well, double-well and double-hump Pol-Dufing equations are studied in this paper. Chebyshev Neural Network (ChNN) model will be applied to obtain numerical solutions these types for first time. hidden layer eliminated by expanding input pattern polynomials which employs single neural ne...

This article deals with the unsteady flow in rotating circular plates located at a finite distance filled Reiner-Rivlin nanofluid. The nanofluid is electrically conducting and incompressible. Furthermore, also accommodates motile gyrotactic microorganisms under effect of activation energy thermal radiation. mathematical formulation performed by employing transformation variables. finalized form...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

the present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. the proposed scheme is based on laplace transform and new homotopy perturbation methods. the fractional derivatives are considered in caputo sense. to illustrate the ability and reliability of the method some examples are provided. the results ob...