We develop a rapid and accurate contour method for the solution of time-fractional PDEs. The inverts Laplace transform via an optimised stable quadrature rule, suitable infinite-dimensional operators, whose error decreases like $\exp(-cN/\log(N))$ $N$ points. is parallisable, avoids having to resolve singularities as $t\downarrow 0$, large memory consumption that can be challenge time-stepping ...

In this article, we use the homotopy perturbation method and Adomian decomposition with Yang transformation to discover analytical solution time-fractional coupled Schrödinger–KdV equation. Caputo sense, fractional derivatives are described. A convergent series is used calculate solutions of PDEs. Analytical results achieved applying techniques numerically calculated represented in form tables ...

In this work, we have applied the variational iteration method and He’s polynomials to solve partial differential equation (PDEs) with time-fractional derivative. The variational homotopy perturbation iteration method (VHPIM) is presented in two steps. Some illustrative examples are given in order to show the ability and simplicity of the approach. All numerical calculations in this manuscript ...

Existing numerical methods for fractional PDEs suffer from low accuracy and inefficiency in dealing with three-dimensional problems or with long-time integrations. We develop a unified and spectrally accurate Petrov–Galerkin (PG) spectral method for a weak formulation of the general linear Fractional Partial Differential Equations (FPDEs) of the form 0D t u + d j=1 c j [a jD 2μ j x j u ] + γ u...

We prove a discrete analogue for the composition of fractional integral and Caputo derivative. This result is relevant in numerical analysis PDEs when one discretizes derivative with so-called L1 scheme. The proof based on asymptotic evaluation sums use Euler-Maclaurin summation formula.