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...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...

in this paper, first the properties of one and two-dimensional differential transforms are presented.next, by using the idea of differential transform, we will present a method to find an approximate solution fora volterra integro-partial differential equations. this method can be easily applied to many linear andnonlinear problems and is capable of reducing computational works. in some particu...

in this paper, operational matrices of riemann-liouville fractional integration and caputo fractional differentiation for shifted jacobi polynomials are considered. using the given initial conditions, we transform the fractional differential equation (fde) into a modified fractional differential equation with zero initial conditions. next, all the existing functions in modified differential equ...

in this paper, we study the numerical solution of hybrid fuzzy differential equations by using differential transformation method (dtm). this is powerful method which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. several numerical examples are given and by comparing the numerical results obtained from dtm  and  predi...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

The objective of this study is to present a mathematical modeling and solution approach for the drying process of spheroidal solids with the application of microwave in capillary porous media based on the Luikov equations, composed of a system of linear and coupled partial differential equations arising from the energy, mass and pressure balances inside the solid matrix. Additionally, the power...

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...

in this study, the vibration of cracked plates is investigated using the differential quadrature method and experimental modal analysis. the crack, which is assumed to be open, is modeled by the extended rotational spring. with its finite length, the crack divides the plate into six segments. then, the differential quadrature is applied to the governing differential equations of motion and the ...