Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators
TLDR
In this paper, a comparison between the local fractional Adomian decomposition (LFAAD) and LFAFL decomposition was performed for solving the Laplace equation. But the results illustrate the significant features of the two methods which are both very effective and straightforward for solving differential equations with local fractionals derivative.Abstract:
We perform a comparison between the local fractional Adomian decomposition and local fractional function decomposition methods applied to the Laplace equation. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.read more
Citations
More filters
Journal ArticleDOI
Characteristic equation method for fractal heat-transfer problem via local fractional calculus
TL;DR: In this paper, a non-differentiable type solution of the heat-transfer equation is obtained, and the characteristic equation method is proposed as a powerful technology to illustrate the analytical solutions of the partial differential equation in fractal heat transfer.
Journal ArticleDOI
A Local Fractional Elzaki Transform Decomposition Method for the Nonlinear System of Local Fractional Partial Differential Equations
TL;DR: In this article , the nonlinear system of local fractional partial differential equations is solved via Local fractional Elzaki transform decomposition (LFT decomposition) method, which combines a LFT and the Adomian decomposition method.
Journal ArticleDOI
Exact solutions for linear systems of local fractional partial differential equations
TL;DR: In this paper, the authors apply the local fractional sumudu decomposition method to solve linear systems of local fractionals partial differential equations, which can be easily applied to many problems and it is capable of reducing the size of computational work to find non-differentiable solutions for similar problems.
Journal ArticleDOI
Local fractional functional decomposition method for solving local fractional Poisson equation in steady heat-conduction problem
TL;DR: In this paper, the analytical solution of the local fractional Poisson equation is obtained for the steady heat-conduction problem via local fraction fractional derivative, and the analytical solutions of the partial differential equation in steady heatconduction are obtained.
Journal ArticleDOI
Local Fractional Sumudu Variational Iteration Method for Solving Partial Differential Equations with Local Fractional Derivative
TL;DR: The Local Fractional Sumudu Variational Iteration Method (LFSVIM) as discussed by the authors was proposed to solve linear and non-linear local fractional partial differential equations.
References
More filters
Book
Fractional Calculus: Models and Numerical Methods
TL;DR: A survey of numerical methods to solve Fractional Variational Equations can be found in this paper, with a focus on CCTRW. Generalized Stirling Numbers of First and Second Kind in the framework of fractional Calculus.
Journal ArticleDOI
Fractional Schrödinger equation.
TL;DR: The Hermiticity of the fractional Hamilton operator and the parity conservation law for fractional quantum mechanics are established and the energy spectra of a hydrogenlike atom and of a fractional oscillator in the semiclassical approximation are found.
Journal ArticleDOI
Fractional diffusion and wave equations
W. R. Schneider,W. Wyss +1 more
TL;DR: In this article, the Green's function of fractional diffusion is shown to be a probability density and the corresponding Green's functions are obtained in closed form for arbitrary space dimensions in terms of Fox functions and their properties are exhibited.
Book
Partial differential equations : methods and applications
TL;DR: In this article, the newly developed Adomian decomposition method along with its modification and some traditional techniques are described and revised, and the new method is described. But the method is not discussed.