The aim of this paper is by using the fractional complex transform and the optimal homotopy analysis by method (OHAM) to find the analytical approximate solutions for nonlinear partial fractional differential Zakharov-Kuznetsov equation. Fractional complex transformation is proposed to convert nonlinear partial fractional differential Zakharov-Kuznetsov equation to nonlinear partial differentia...

In the present study a new method is proposed that allows the derivation of control laws capable of enforcing the desirable dynamics on an invariant manifold in state space. The problem of interest naturally surfaces in broad classes of physical and chemical systems whose dynamic behavior needs to be controlled and favorably shaped by external driving forces. In particular, the formulation of t...

A posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations Abstract This paper presents constructive a posteriori estimates of inverse operators for boundary value problems in linear elliptic partial differential equations (PDEs) on a bounded domain. This type of estimates plays an important role in the numerical verification of the...

For families of partial differential equations (PDEs) with particular boundary conditions, strict Lyapunov functions are constructed. The PDEs under consideration are parabolic and, in addition to the diffusion term, may contain a nonlinear source term plus a convection term. The boundary conditions may be either the classical Dirichlet conditions, or the Neumann boundary conditions or a period...

The term of multitime soliton has recently been coined in our research school to describe a multitime pulselike nonlinear wave (multitime solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed vector. To introduce this notion, it was necessary to introduce multitime PDEs that extend solitonic single-time PDEs via geometrical ingredients. This paper c...