The prevalence of the use of mathematical software has dramatically influenced the
evolution of differential equations. The use of these useful tools leads to faster advances in …

Abstract Objective: New generalized Schrödinger equations with polynomial nonlinearities
are considered. The Cauchy problem for these equations cannot be solved by the inverse …

Application of transformations for dependent and independent variables is used for finding
solitary wave solutions of the generalized Schrödinger equations. This new form of equation …

Abstract Objective: The generalized Schrödinger–Hirota equation of the fourth order is
considered using the traveling wave solutions. Method: The compatibility of the …

Abstract Objective: The Generalized Schrödinger–Hirota equation with an arbitrary power of
nonlinearity is studied. Method: The compatibility of the overdetermined system of equation …

In this study, we solve the fractional advection–dispersion equation (FADE) by applying the
Laplace transform decomposition method (LTDM) and the variational iteration transform …

In this work, a new generalized concept of conformable derivative is given and named
generalized θ–conformable derivative (GTCD). Several properties are studied such as the …

In this work, we consider the stochastic fractional‐space Kuramoto–Sivashinsky equation
using conformable derivative. The Riccati equation method is used to get the analytical …

In this work, we utilize a new generalized derivative of conformable type to examine the
nonlinear evolution equations in a Wick-type stochastic environment. By a new auxiliary …

This paper considers deriving new exact solutions of a nonlinear complex generalized
Zakharov dynamical system for two different definitions of derivative operators called …