THE MODIFIED FRACTIONAL POWER SERIES FOR SOLVING A CLASS OF FRACTIONAL STURM-LIOUVILLE EIGENVALUE PROBLEMSAbstract
Vol. 10 (1). Jan. 2019, No. 13, pp. 154-166
M.I. SYAM, M. ALQURAN, H.M. JARADAT, S. AL-SHARA’
Abstract. This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional 2α-order Sturm-Liouville problem where 1 2 < α ≤ 1. In this paper, we implement the modiﬁed fractional power series (MFPS) method to approximate the eigenvalues. To ﬁnd the eigenvalues, we force the approximate solution produced by the MMPS method satisﬁes the boundary condition at x = 1. The fractional derivative is described in the Caputo sense. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the eigenfunctions of the proposed problem. The convergence of the approximate eigenfunctions produced by the MFPS to the exact eigenfunctions is proven.