Interpolating Stabilized Element Free Galerkin Method for Neutral Delay Fractional Damped Diffusion-Wave Equation

Abstract

A numerical solution for neutral delay fractional order partial differential equations involving the Caputo fractional derivative is constructed. In line with this goal, the drift term and the time Caputo fractional derivative are discretized by a finite difference approximation. The energy method is used to investigate the rate of convergence and unconditional stability of the temporal discretization. The interpolation of moving Kriging technique is then used to approximate the space derivative, yielding a meshless numerical formulation. We conclude with some numerical experiments that validate the theoretical findings.

Stability and asymptotics for fractional delay diffusion‐wave equations

“…By substituting the estimates ( 13), (14), and ( 15) into (12) and choosing a sufficiently large T 1 , we obtain…”

“…For time-dependent mod-els, delay happens everywhere because of the transportation of energies and materials [10][11][12]. Recently, fractional delay diffusion-wave equations have attracted growing interest of the research community (see [13][14][15][16][17]). Generally speaking, the appearance of delay will change the original properties of the equations.…”

The μ-neutral fractional multi-delayed differential equations

“…They are very often exploited in propagation of energy or information and transport in interdependent systems (see e.g. [1,6,16] and reference therein). In reference [7], Khusainov and Shuklin were able to find a solution of the below linear fractional delayed differential system in terms of producing the delayed exponential matrix.…”

The $μ$-neutral fractional multi-delayed differential equations

“…They are very often exploited in propagation of energy or information and transport in interdependent systems (see e.g. [1], [2], [3] and reference therein). In reference [8], Khusainov and Shuklin were able to find a solution of the below linear fractional delayed differential system in terms of producing the delayed exponential matrix.…”

“…The drawback of system (1) is to assume that the coefficient matrices B and F must be commutative. In reference [9], Li and Wang consider the fractional version of system (1) in the case of F = Θ. The drawback is also in progress because of validation of commutativity of coefficient matrices when F = Θ.…”