Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem

Abstract

A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy

Implementation and Convergence Analysis of Homotopy Perturbation Coupled With Sumudu Transform to Construct Solutions of Local-Fractional PDEs

“…For example, local fractional Laplace equation [15], diffusion equations on Cantor sets [25], Korteweg-ed Vries equation with local fraction operator [26] and fractal heat conduction equation [27] as well as fractal wave equation [28].…”

Exact solutions for linear systems of local fractional partial differential equations

“…Recently, there appeared a large part of scientific research concerning local fractional differential equations or local fractional partial differential, adopted in its entirety on the above mentioned methods to solve this new types of equations. For example, among these research we find, local fractional Adomian decomposition method ( [9], [10], [15]), local fractional homotopy perturbation method ( [11], [12]), local fractional homotopy perturbation Sumudu transform method [13], local fractional variational iteration method ( [14], [15]), local fractional variational iteration transform method ( [16]- [18]), local fractional Fourier series method ( [19]- [21]), Laplace transform series expansion method [22], local fractional Sumudu transform method ( [23], [24]), local fractional Sumudu transform series expansion method ( [25], [26]), local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative [27].…”

A new numerical technique for local fractional diffusion equation in fractal heat transfer

“…Several approaches were developed to find the numerical and analytical solutions for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), namely the methods of Mellin and Laplace transforms [5], implicit local radial basis function (ILRBF) [19], finite difference (FD) [32], homotopy perturbation (HP) [18], homotopy analysis (HA) [10], heat-balance integral (HBI) [15], variational iteration (VI) [14], generalized differential transform (GDT) [29], and others [9,22,25,31]. There are distinct strategies for solving the local fractional partial differential equations [13,20,34,35], such as the local fractional perspectives to differential transform (DT) [8], variation iteration method (VIM) [36], Fourier transform (FT) [39], Laplace transform (LT) [40], Laplace variation iteration method (LVIM) [21], and functional method (FM) [6].…”