The current manuscript examines the effect of the fractional temporal variation on the
vibration of waves on non-homogeneous elastic substrates by applying the Laplace integral …

The aim of this paper is to implement the high-order local discontinuous Galerkin method
(LDGM) for solving partial integro-differential equations (PIDEs) in two dimensions. Time …

This paper is dedicated to proposing two numerical algorithms for solving the one‐and two‐
dimensional heat partial differential equations (PDEs). In these algorithms, generalized …

In this paper, the Laplace transform combined with the local discontinuous Galerkin method
is used for distributed‐order time‐fractional diffusion‐wave equation. In this method, at first …

The Laplace transform is a central mathematical tool for analysing 1D/2D signals and for the
solution to PDEs; however, its definition and computation on arbitrary data is still an open …

It is well known that major error occur in the time integration instead of the spatial
approximation. In this work, anisotropic kernels are used for temporal as well as spatial …

In this paper, we solve the fractional differential equations (FDEs) with boundary value
conditions in Sobolev space Hn [0, 1]. The strategy is constructing multiscale orthonormal …

‎ This paper deals with a time-space fractional Schrödinger equation with homogeneous
Dirichlet boundary conditions‎.‎ A common strategy for discretizing time-fractional operators is …

In approximating time-dependent partial differential equations, major error always occurs in
the time derivatives as compared to the spatial derivatives. In the present work the time and …

Multi-term fractional diffusion equations can be regarded as a generalisation of fractional
diffusion equations. In this paper, we develop an efficient meshless method for solving the …