In this study‎, ‎an efficient method is presented for solving infinite boundary integro-differential equations (IBI-DE) of the second kind with degenerate kernel in terms of Laguerre polynomials‎. ‎Properties of these polynomials and operational matrix of integration are first presented‎. ‎These properties are then used to transform the integral equation to a matrix equation which corresponds t...

In this letter we develop a new generalization of the two-dimensional differential transform method that will extend the application of the method to linear partial differential equations with spaceand time-fractional derivatives. The new generalization is based on the two-dimensional differential transform method, generalized Taylor’s formula and Caputo fractional derivative. Several illustrat...

this paper has been devoted to apply the reconstruction of variational iteration method (rvim) to handle the systems of integro-differential equations. rvim has been induced with laplace transform from the variational iteration method (vim) which was developed from the inokuti method. actually, rvim overcome to shortcoming of vim method to determine the lagrange multiplier. so that, rvim method...

and Applied Analysis 3 3. Two-Dimensional Differential Transform Method The two-dimensional differential transform of function w(x, y) is defined as W(k, h) = 1 k!h! [ ∂ k+h w (x, y) ∂x∂y ] x=0 y=0 , (9) where it is noted that upper case symbol W(k, h) is used to denote the two-dimensional differential transform of a function represented by a corresponding lower case symbol w(x, y). The differe...