This paper describes an analytical approach to conduct analysis of beam-column elements with generalized end-boundary conditions on a homogeneous or non-homogeneous Pasternak elastic foundation. The mathematical formulation utilized herein is that presented by the senior author in recent work. differential equation (DE) governing behavior element solved using transformation method (DTM). DTM of...

The atomic force microscope system (AFM) has become a popular and useful instrument to measure the intermolecular forces with atomic resolution that can be applied in electronics, biological analysis, materials, semiconductors, etc. This paper studies the bifurcation phenomenon and complex nonlinear dynamic behavior of the probe tip between the sample and microcantilever of an atomic force micr...

Differential transformation method is used to find the solution of the seventh order boundary value problem. The approximate solution of the problem is calculated in the form of a rapid convergent series. Two numerical examples have been considered to illustrate the efficiency and implementation of the method and the results are compared with the method developed in [15].

Abstract In this paper, we focus on the two-dimensional linear Telegraph equation with some initial and boundary conditions. We transform the model of partial differential equation (PDE) into a system of first order, linear, ordinary differential equations (ODEs). Our method is based on finding a solution in the form of a polynomial in three variables Un(x, y, t) = ∑n i=0 ∑n j=0 ∑n k=0 U(i, j, ...

In this paper, the projective Riccati equation method is applied to find exact solutions for fractional partial differential equations in the sense of modified RiemannLiouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the vali...