Approximate solutions of inverse Nodal problem with conformable derivative

Document Type : Research Paper

Authors

1 Department of Mathematics, Jouybar Branch, Islamic Azad University, Jouybar, Iran.

2 Department of Mathematics, Neka Branch, Islamic Azad University, Neka, Iran.

Abstract

Our research is about the Sturm-Liouville equation which contains conformable fractional derivatives of order $\alpha \in (0,1]$ in lieu of the ordinary derivatives. First, we present the eigenvalues, eigenfunctions, and nodal points, and the properties of nodal points are used for the reconstruction of an integral equation. Then, the Bernstein technique was utilized to solve the inverse problem, and the approximation of solving this problem was calculated. Finally, the numerical examples were introduced to explain the results. Moreover,  the analogy of this technique is shown in a numerical example with the Chebyshev interpolation technique .

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