scholarly journals SOLUTIONS OF FRATIONAL EMDEN-FOWLER EQUATIONS BY HOMOTOPY ANALYSIS METHOD

2018 ◽  
Vol 13 (1) ◽  
pp. 7042-7047 ◽  
Author(s):  
Huan Huan Wang ◽  
Yue Hu
Keyword(s):  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis

In this paper, we have solved the singular initial value problems of fractional Emden-Fowler type equations by using the homotopy analysis method. The approximate analytical solution of this type equations are obtained.

scholarly journals Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

2019 ◽  
Vol 33 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Ali Kurt ◽  
Orkun Tasbozan
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Modified Burgers Equation ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

AbstractIn this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (HAM).

scholarly journals Solutions of the heat-conduction model described by fractional Emden-Fowler type equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 113-120 ◽  
Author(s):  
Chunfu Wei ◽  
Huanhuan Wang
Keyword(s):  
Heat Conduction ◽  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Approximate Solutions ◽  
Time Dependent ◽  
Analysis Method ◽  
Initial Value ◽  
Conduction Model ◽  
Homotopy Analysis

In this paper, we presented a reliable algorithm to solve the singularity initial value problems of the time-dependent fractional Emden-Fowler type equations by homotopy analysis method. The approximate solutions of the problems are obtained.

scholarly journals A New Piecewise-Spectral Homotopy Analysis Method for Solving Chaotic Systems of Initial Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
H. Saberi Nik ◽  
Sohrab Effati ◽  
Sandile S. Motsa ◽  
Stanford Shateyi
Keyword(s):  
Homotopy Analysis Method ◽  
Initial Value Problems ◽  
System Modeling ◽  
Equation System ◽  
Analysis Method ◽  
Initial Value ◽  
Homotopy Analysis ◽  
Highly Oscillatory ◽  
First Time ◽  
Spectral Homotopy Analysis Method

An accurate algorithm for solving initial value problems (IVPs) which are highly oscillatory is proposed. The proposed method is based on a novel technique of extending the standard spectral homotopy analysis method (SHAM) and adapting it to a sequence of multiple intervals. In this new application the method is referred to as the piecewise spectral homotopy analysis method (PSHAM). The applicability of the proposed method is examined on the differential equation system modeling HIV infection of CD4+T cells and the Genesio-Tesi system which is known to be chaotic and highly oscillatory. Also, for the first time, we present here a convergence proof for SHAM. We treat in detail Legendre collocation and Chebyshev collocation. The method is compared to MATLAB’sode45inbuilt solver as a measure of accuracy and efficiency.

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