It is well known that fractional differential equations appeared more and more frequently in different research areas, such as fluid mechanics, viscoelasticity, biology, physics, engineering and other areas of science [1-30]. Considerable attention have been spent in recent years to develop techniques to look for solutions of nonlinear fractional partial differential equations (NFPDEs). Consequ...

In this paper, the variational iteraton method is used for solving the Generalized HirotaSatsuma Coupled KdV ( GHS KdV ) equations. In this method general Lagrange multipliers are introduced to construct correction functionals for the models.In the current paper, we are applied this technique on interesting and important model.The results are compared with exact solution.

Model construction for different physical situations, and developing their solutions, are the major characteristics of scientific work in physics engineering. Korteweg–de Vries (KdV) models very important due to ability capture situations such as thin film flows waves on shallow water surfaces. In this work, a new approach predicting analyzing nonlinear time-fractional coupled KdV systems is pr...

Recently, many nonlinear coupled evolution equations, such as the coupled Korteweg–de Vries (KdV) equation, the coupled Boussinesq equation, and the coupled mKdV equation, appear in scientific applications [1 – 13]. The coupled evolution equations attracted a considerable research work in the literature. The aims of these works have been the determination of soliton solutions and the proof of c...

A new iterative technique is employed to solve a system of nonlinear fractional partial differential equations. This new approach requires neither Lagrange multiplier like variational iteration method VIM nor polynomials like Adomian’s decomposition method ADM so that can be more easily and effectively established for solving nonlinear fractional differential equations, and will overcome the li...

This paper focuses on the exact soliton solutions of (2+1)-dimensional generalized Hirota–Satsuma–Ito equations with time-dependent linear phase speed. Based Painlevé integrability test this equation, condition is determined. Then general N-soliton are constructed by Hirota bilinear method. Not only expressions and their degenerations, but also spatial structures presented for different choices...

Abstract In this article, through the Hirota bilinear method and long wave limit method, based on N-solitons, we construct multiple lump solutions of generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding obtained, further elucidate physical implications these with three-dimensional two-dimensional graphs. The obtained might have practical applicati...