.... Design/methodology/approach The principle of scaling analysis is used to reformulate the governing equations into a dimensionless partial differential equations (PDEs). Moreover, the PDEs are analytically solved by the application of Laplace transformation, and the impact of physical parameters...

... a fractional order of heat transport to address this issue. Design/methodology/approach The employment of the matrix exponential method, which forms the basis of the state-space approach in contemporary theory, is central to this strategy. The resulting formulation, together with the Laplace transform...

... show that the proposed approach is highly authentic and reliable for the fractional-order models. Design/methodology/approach The Laplace transform residual power series method (ℒT-RPSM) is the combination of Laplace transform (ℒT) and residual power series method (RPSM). The ℒT is examined...

... on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems...

.... If h ( t ) = t γ , then Laplace transform is as follows: Muhammad Nadeem can be contacted at: nadeem@mail.dlut.edu.cn 07 02 2020 11 06 2020 20 06 2020 © Emerald Publishing Limited 2020 Emerald Publishing Limited Licensed re-use rights only Caputo...

... solution. The derived results demonstrate that this scheme is very effective. Finally, the convergence of this method is discussed. Findings A traditional method is combined with the Laplace transform to construct this scheme. To decompose the nonlinear terms, this paper introduces the homotopy...

...Ji-Huan He; Habibolla Latifizadeh Purpose The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM). Design/methodology/approach Firstly, the Laplace transform technique is used to reconstruct the variational...

... of the Laplacian matrix of the graph, to partition it into three subgraphs and correspondingly trisect the finite element model. © MCB UP Limited 2001 Graph theory Algebraic model Laplace transform Genetic algorithms Parallel processing provides considerable computational power...

... and convection. Thus, we can assume that inside the particle and at a sufficiently large distance from it: (1) © MCB UP Limited 1998 Heat conduction Laplace transform Particulates Photothermal wave Pulse (11) An analytical solution of (11) cannot be found...