scholarly journals Two-scale transform for two-dimensional fractal heat equation in a fractal space

2021 ◽  
pp. 124-124
Author(s):  
Chun-Fu Wei
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Equation ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Fractal Model ◽  
Two Dimensional ◽  
Homotopy Perturbation ◽  
Fractal Derivative ◽  
Fractal Space

A two-dimensional fractal heat conduction in a fractal space is considered by He?s fractal derivative. The two-scale transform is adopted to convert the fractal model to its differential partner. The homotopy perturbation method is used to find the approximate analytical solution.

scholarly journals Approximate analytical solution for Phi-four equation with he’s fractal derivative

2021 ◽  
pp. 127-127
Author(s):  
Shuxian Deng ◽  
Xinxin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Integral Transform ◽  
Approximate Analytical Solution ◽  
Homotopy Perturbation ◽  
Fractal Derivative ◽  
Fractal Differential Equations ◽  
First Time

This paper, for the first time ever, proposes a Laplace-like integral transform, which is called as He-Laplace transform, its basic properties are elucidated. The homotopy perturbation method coupled with this new transform becomes much effective in solving fractal differential equations. Phi-four equation with He?s derivative is used as an example to reveal the main merits of the present technology.

scholarly journals A Novel Homotopy Perturbation Algorithm Using Laplace Transform for Conformable Partial Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Sajad Iqbal ◽  
Mohammed K. A. Kaabar ◽  
Francisco Martínez
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Laplace Transform ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Partial Differential ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
Different Types

In this article, the approximate analytical solutions of four different types of conformable partial differential equations are investigated. First, the conformable Laplace transform homotopy perturbation method is reformulated. Then, the approximate analytical solution of four types of conformable partial differential equations is presented via the proposed technique. To check the accuracy of the proposed technique, the numerical and exact solutions are compared with each other. From this comparison, we conclude that the proposed technique is very efficient and easy to apply to various types of conformable partial differential equations.

scholarly journals He’s fractal calculus and its application to fractal KdV equation

2021 ◽  
pp. 100-100
Author(s):  
Xue-Si Ma ◽  
Li-Na Zhang
Keyword(s):  
Analytical Solution ◽  
Iteration Method ◽  
Approximate Analytical Solution ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Natural Phenomena ◽  
Transform Method ◽  
Fractal Derivative ◽  
Fractal Calculus ◽  
Fractal Space

He?s fractal calculus is a powerful and effective tool to dealing with natural phenomena in a fractal space. In this paper, we study the fractal KdV equation with He?s fractal derivative. We first adopt the two-scale transform method to convert the fractal KdV equation into its traditional partner in acontinuous space. Finally, we successfully use He?s variational iteration method (HVIM) to obtain its approximate analytical solution.

scholarly journals An Approximate Analytical Solution Of Nonlinear Equations In N-Aminopiperidine Synthesis: New Approach Of Homotopy Perturbation Method)

2021 ◽  
Vol 12 (1S) ◽  
pp. 595-605
Author(s):  
R. Joy Salomi, Et. al.
Keyword(s):  
Analytical Solution ◽  
Perturbation Method ◽  
Nonlinear Equations ◽  
Homotopy Perturbation Method ◽  
Approximate Analytical Solution ◽  
Rate Equations ◽  
Simple Analytical Expression ◽  
New Approach ◽  
Homotopy Perturbation ◽  
Numerical Result

the synthesis of N-aminopiperidine (NAPP) using hydroxylamine-O-sulfonic acid (HOSA) is based on system of nonlinear rate equations. The new approach to homotopy perturbation method is applied to solve the nonlinear equations. A simple analytical expression for concentrations of hydroxylamine-O-sulfonique acid (HOSA), piperidine (PP), N-aminopiperidine (NAPP), sodium hydroxide (NaOH) and diazene (N2H2) along with NAPP yield is obtained and is compared with numerical result. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. The obtained analytical result of NAPP yield is compared with the experimental results. The influence of reagents ratio p and rate constants ratio r on yield has been discussed.

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