We consider the distributed-order space-time fractional heat type equation \begin{document}$ \mathbb{D}^{(\nu)}u(t, x) = -(-\Delta)^{\alpha/2}u(t, x), \ t>0, x\in D, $\end{document} where$ \mathbb{D}^{(\nu)} $ is derivative based on Caputo time-fractional derivative, -(-\Delta)^{\alpha/2} generator of an isotropic stable process for \alpha\in(0, 2] $, D a bounded domain in \mathbb{R}^d and \...

In search of the exact solutions nonlinear partial differential equations in solitons form has become most popular to understand internal features physical phenomena. this paper, we discovered various type for conformable space-time Schrodinger equation (CSTNLSE) with Kerr law nonlinearity. To seek such solutions, applied two proposed methods which are Sardar-subequation method and new extended...

This paper gathers the tools for solving Riemann-Liouville time fractional non-linear PDE’s by using a Galerkin method. method has advantage of not being more complicated than one used to solve same PDE with first order derivative. As model problem, existence and uniqueness is proved semilinear heat equations polynomial growth at infinity.

When a time-dependent partial differential equation (PDE) is discretized in space with a spectral approximation, the result is a coupled system of ordinary differential equations (ODEs) in time. This is the notion of the method of lines (MOL), and the resulting set of ODEs is stiff; the stiffness may be even exacerbated sometimes. The linear terms are the primarily responsible for the stiffness...