The Homotopy Analysis Method was introduced in S. Liao’s Ph.D. thesis in 1992 and has had great success in solving nonlinear differential equations since. For the nonlinear equation one introduces auxiliary linear operator with and a new parameter and considers the family of equations . This new family has formally the property that its solution deforms from of the linear operator $L$ to that of $Nu=0$ at . This is a very general infrastructure where then the solution of the original equation is obtained by a Taylor expansion in
and then the solution to the original problem is obtained by determining $u_k(x)$ by differentiations in and setting .
small step toward understanding instability of solutions of nonlinear fractional diffusions