Eigenvalues of fractional Sturm-Liouville problems by successive method

In this paper, we consider a fractional Sturm-Liouville equation of the form, cD 0+ D 0+y(t) + q(t)y(t) = y(t); 0 < < 1; t 2 [0; 1]; with Dirichlet boundary conditions I1 0+ y(t)jt=0 = 0; and I1 0+ y(t)jt=1 = 0; where, the sign is composition of two operators and q 2 L2(0; 1), is a real-valued potential function. We use a recursive method based on Picard's successive method to nd the solution of this problem. We prove the method is convergent and show that the eigenvalues are obtained from the zeros of the Mittag-Leffer function and its derivatives.