scholarly journals On Analytical Solution of Time-Fractional Type Model of the Fisher’s Equation

2020 ◽  
pp. 1419-1425
Author(s):  
Shaheed N. Huseen
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Homotopy Analysis Method ◽  
Type Model ◽  
Analysis Method ◽  
Fisher’S Equation ◽  
Fisher's Equation ◽  
Homotopy Analysis ◽  
The Laplace Transform ◽  
Fractional Type

In this paper, the time-fractional Fisher’s equation (TFFE) is considered to exam the analytical solution using the Laplace q-Homotopy analysis method (Lq-HAM)”. The Lq-HAM is a combined form of q-homotopy analysis method (q-HAM) and Laplace transform. The aim of utilizing the Laplace transform is to outdo the shortage that is mainly caused by unfulfilled conditions in the other analytical methods. The results show that the analytical solution converges very rapidly to the exact solution.

scholarly journals Analytical solution of Velocities and Temperature fields using Homotopy Analysis Method

2021 ◽  
Vol 12 (1S) ◽  
pp. 691-700
Author(s):  
Dr. K.V.Tamil Selvi , Et. al.
Keyword(s):  
Partial Differential Equations ◽  
Analytical Solution ◽  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Temperature Fields ◽  
Analysis Method ◽  
Partial Differential ◽  
Convective Boundary ◽  
Homotopy Analysis

In this paper, analysis of nonlinear partial differential equations on velocities and temperature with convective boundary conditions are investigated. The governing partial differential equations are transformed into ordinary differential equations by applying similarity transformations. The system of nonlinear differential equations are solved using Homotopy Analysis Method (HAM). An analytical solution is obtained for the values of Magnetic parameter M2, Prandtl number Pr, Porosity parameter

A New Semi-Analytical Solution of the Telegraph Equation with Integral Condition

2011 ◽  
Vol 66 (12) ◽  
pp. 760-768 ◽  
Author(s):  
S. Abbasbandy ◽  
H. Roohani Ghehsarehb
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iterative Algorithm ◽  
Homotopy Analysis Method ◽  
Integral Condition ◽  
Telegraph Equation ◽  
Current Work ◽  
Analysis Method ◽  
Numerical Examples ◽  
Homotopy Analysis

In the current work, the telegraph equation in its general form and with an integral condition is investigated. Also the well-known homotopy analysis method (HAM) is applied and an interesting iterative algorithm is proposed for solving the problem in general form. Some numerical examples are given and compared with the exact solution to show the effectiveness of the proposed method.

scholarly journals Homotopy Analysis Method for Solving Foam Drainage Equation with Space- and Time-Fractional Derivatives

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Hadi Hosseini Fadravi ◽  
Hassan Saberi Nik ◽  
Reza Buzhabadi
Keyword(s):  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Convergent Series ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Foam Drainage Equation ◽  
Foam Drainage

The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.

Nonlinear dynamics of MEMS/NEMS resonators: analytical solution by the homotopy analysis method

2016 ◽  
Vol 23 (6) ◽  
pp. 1913-1926 ◽  
Author(s):  
Farid Tajaddodianfar ◽  
Mohammad Reza Hairi Yazdi ◽  
Hossein Nejat Pishkenari
Keyword(s):  
Nonlinear Dynamics ◽  
Analytical Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Homotopy Analysis

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).

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