We use the fractional transformation to convert the nonlinear partial fractional differential equations with the nonlinear ordinary differential equations. The Exp-function method is extended to solve fractional partial differential equations in the sense of the modified Riemann-Liouville derivative. We apply the Exp-function method to the time fractional Sharma-Tasso-Olver equation, the space ...

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...

We propose a new method for constructing exact solutions to nonlinear delay reaction–diffusion equations of the form ut = kuxx + F (u,w), where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = ∑N n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or fun...

The connection of curves and surfaces in R3 to some nonlinear partial differential equations is very well known in differential geometry [1], [2]. Motion of curves on two dimensional surfaces in differential geometry lead to some integrable nonlinear differential equations such as nonlinear Schrödinger (NLS) equation [3], Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations [...

Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give th...

An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for variants of the KdV–Burger and the K(n, n)–Burger equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching exac...

mhd boundary layer flow of two phase model nanofluid over a vertical plate is investigated both analytically and numerically. a system of governing nonlinear partial differential equations is converted into a set of nonlinear ordinary differential equations by suitable similarity transformations and then solved analytically using homotopy analysis method and numerically by the fourth order rung...