LAUSR

where A, a, and r are constants, ( , ) f x t and ( ) g y are the given functions, and D ( 0) α α > is the fractional derivative in Caputo sense, see, for example, [1-6]. When 1 α = , eq. (1) was adopted to describe the heat-conduction model of the human head [7]. The singularity behavior that occurs at the origin is the main difficulty in the analysis of eqs. (1) and (2). Recently, several researchers discussed such initial value problems [7-11]. Various numerical methods, such as, were applied to this kind of the initial value problems, see [12-20] and the cited references therein. The purpose of the present work is to use the homotopy analysis method (HAM) [7, 12] to obtain the approximate analytical solutions of eq. (1).