An Application of the Homotopy Analysis Method for the Time- or Space-Fractional Heat Equation

This paper focuses on the usage of homotopy analysis method (HAM) to solve fractional heat conduction equation. In presented mathematical model, Caputo-type derivatives over time or space are considered. HAM, it is not necessary discretize considered domain, which its great advantage. As a result method, continuous function obtained, can be used for further analysis. For first time, equations, we proved that if series created in converges, then sum solution A sufficient condition this convergence provided, as well an estimation error approximate solution. also presents examples illustrating accuracy and stability proposed algorithm.