In this paper, we study the approximate solution of two-dimensional nonlinear Volterra integral equations by two-dimensional differential transform method. New theorems for the transformation of integrals are introduced and proved. We will give an applicable relation between the two-dimensional nonlinear Volterra integral equations and two-dimensional differential transformation, in order to so...

In this paper, we apply the local fractional Laplace transform method (or Yang-Laplace transform) on Volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative operators. This approach provides us with a convenient way to find a solution ...

In this paper, we compile the fractional power series method and Laplace transform to design a new algorithm for solving Volterra integro-differential equation. For that, assume (LPS) solution in terms of q=1m,m∈Z+, where derivative order α=qγ, which γ∈Z+. This assumption will help us write integral, kernel, nonhomogeneous as LPS with same power. The recurrence relations finding coefficients ca...

We review here various recent applications of Wassertein–type metrics to both nonlinear partial differential equations and integro–differential equations. Among others, we can describe the asymptotic behavior of nonlinear friction equations arising in the kinetic modelling of granular flows, and the growth of the support in nonlinear diffusion equations of porous medium type. Further examples i...