<p style='text-indent:20px;'>We consider optimal control of fractional in time (subdiffusive, i.e., for <inline-formula><tex-math id="M1">\begin{document}$ 0<\gamma <1 $\end{document}</tex-math></inline-formula>) semilinear parabolic PDEs associated with various notions diffusion operators an unifying fashion. Under general assumptions on the nonlinea...

We consider a class of parabolic stochastic PDEs on bounded domains $D\subseteq\mathbb{R}^d$ that includes the heat equation, but with fractional power $\gamma$ Laplacian. Viewing solution as process values in scale Sobolev spaces $H_r$, $r < \gamma - d/2$, we study its variations $H_r$ along regular partitions time-axis. As mesh size tends to zero, find phase transition at $r=-d/2$: solutions ...

Radial Basis Functions (RBFs) have been found to be widely successful for the interpolation of scattered data over the last several decades. The numerical solution of nonlinear Partial Differential Equations (PDEs) plays a prominent role in numerical weather forecasting, and many other areas of physics, engineering, and biology. In this paper, Differential Quadrature (DQ) method- based RBFs are...

We put into practice relatively new analytical techniques, the Shehu decomposition method and iterative transform method, for solving nonlinear fractional coupled Korteweg-de Vries (KdV) equation. The KdV equation has been developed to represent a broad spectrum of physics behaviors evolution association waves. Approximate-analytical solutions are presented in form series with simple straightfo...

In this work we introduce and perform a study on the multitime multi-objective fractional variational problem of minimizing a vector of quotients of path independent curvilinear integral functionals (MFP ) subject to certain partial differential equations (PDE) and/or partial differential inequations (PDI), using a geometrical language. The paper is organized as follows: §1 formulates a PDI&PDE...

This study aims to propose numerical schemes for fractional time discretization of partial differential equations (PDEs). The scheme is comprised two stages. Using von Neumann stability analysis, we ensure the robustness scheme. energy balance model climate change modified by adding source terms. local analysis presented. Also, in form PDEs with effect diffusion given and solved applying propos...

Time fractional PDEs have been used in many applications for modeling and simulations. Many of these are multiscale contain high contrast variations the media properties. It requires very small time step size to perform detailed computations. On other hand, presence spatial grids, is required explicit methods. Explicit methods advantages as we discuss paper. In this paper, propose a partial met...

The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate via certain Monte Carlo simulations. main results represent upper bound errors between exact solution and approximation, estimate fluctuation appropriate central limit theorem (CLT) construction confidence intervals. Moreover, provide rates convergence ...