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 ...

The article proposes a method for analyzing the Cauchy problem wide class of evolutionary linear partial differential equations with variable coefficients. By applying (inverse) Fourier transform, original equation is reduced to an integro-differential equation, which can be considered as ordinary in corresponding Banach space. selection this space carried out such way that principle contractio...

We show that the differential transform is well known Taylor series (contrary to what authors claim) and method (DTM) Frobenius method, commonly used obtain exact or approximate solutions equations. The generalized (GTM) merely application of Padé approximants produced by method. argue particular differential-difference nonlinear equations are scarce utility because initial conditions not flexi...

The main objective of this paper is to use the reduced differential to transform method (RDTM) for finding the analytical approximate solutions of two integral members of nonlinear Kadomtsev–Petviashvili (KP) hierarchy equations. Comparing the approximate solutions which obtained by RDTM with the exact solutions to show that the RDTM is quite accurate, reliable and can be applied for many other...