Related papers: Lie group theory for nonlinear fractional K(m,n) t…

Let $k$ be a differential field of characteristic zero and $E$ be a liouvillian extension of $k$. For any differential subfield $K$ intermediate to $E$ and $k$, we prove that there is an element in the set $K-k$ satisfying a linear…

We study the well-posedness of a semilinear fractional diffusion equation and formulate an associated inverse problem. We determine fractional power type nonlinearities from the exterior partial measurements of the Dirichlet-to-Neumann map.…

Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…

The $k$-symplectic structures appear in the geometric study of the partial differential equations of classical field theories. Meanwhile, we present a new application of the $k$-symplectic structures to investigate a type of systems of…

We introduce families of quasi-rectifiable vector fields and study their geometric and algebraic aspects. Then, we analyse their applications to systems of partial differential equations. Our results explain, in a simpler manner, previous…

This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…

A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…

In this paper we study the analytic solutions of Burgers-type nonlinear fractional equations by means of the Invariant Subspace Method. We first study a class of nonlinear equations directly related to the time-fractional Burgers equation.…

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The…

We analyze the classical equations of motion for a particle moving in the presence of a static magnetic field applied in the $ z $ direction, which varies as $ {1\over{x^2}} $. We find the symmetries through Lie's method of group analysis.…

The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations…

We classify the Lie point symmetries for the 2+1 nonlinear generalized Kadomtsev-Petviashvili equation by determine all the possible f(u) functional forms where the latter depends. For each case the one-dimensional optimal system is…

In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential…

We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…

The paper is devoted to the construction of a probabilistic particle algorithm. This is related to nonlin-ear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential…

We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.

Using Lie group theory and canonical transformations we construct explicit solutions of nonlinear Schrodinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities…

We perform the complete symmetry classification of the Klein-Gordon equation in maximal symmetric spacetimes. The central idea is to find all possible potential functions $V(t,x,y)$ that admit Lie and Noether symmetries. This is done by…

In this paper, we further consider the symmetry-based method for seeking nonlocally related systems for partial differential equations. In particular, we show that the symmetry-based method for partial differential equations is the natural…

We use a one-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain. We also…