### Fractional Homotopy Analysis Transform Method for a Fin Having Temperature Dependent Internal Heat Generation

#### Abstract

*Fractional Homotopy** Analysis Transform Method (FHATM) is a ** **new analytical tool for solving homogeneous and non-homogeneous fin equations. FHATM is **a novel and innovative modification in Laplace Transform Algorithm (LTA) thus making analysis easier. Non-linear problems are solved by proposed technique without using Adomian and He’s polynomial which is a clear benefit of this new algorithm over decomposition and homotopy perturbation transform methods. This is an elementary technique which gives more qualitative difference in analysis between FHATM and other methods. In this paper, it is seen that the auxiliary parameter **ħ,** **which controls the convergence of the HATM approximate series solution, can also be used in predicting and finding multiple solutions. The proposed method is illustrated by solving a fin which has temperature dependent internal heat generation and** **constant** thermal conductivity.** *

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