Abstract
This article is devoted to both theoretical and numerical studies of eigenvalues of regular fractional $2\alpha $-order Sturm-Liouville problem where $\frac{1}{2}< \alpha \leq 1$. In this paper, we implement the reproducing kernel method RKM) to approximate the eigenvalues. To find the eigenvalues, we force the approximate solution produced by the RKM satisfy 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. Uniformly convergence of the approximate eigenfunctions produced by the RKM to the exact eigenfunctions is proven.
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