Homotopy Analysis Method for Solving Fractional Sturm-Liouville Problems

The aim of this paper is to present an efficient and reliable treatment of the homotopy analysis method (HAM) for solving fractional Sturm-Liouville differential equation Dy(t)q(t)y(t) (t)y(t), 12, t[0,1] which the second order derivatives is replaced by a fractional derivative. y(t) is positive and smooth function and Da that denotes the fractional differential operator of order a, is described in the Caputo sense. Several illustrative examples are given to demonstrate effectiveness and reliability of HAM for solving fractional Sturm-Liouville proble