Approximate Solutions of Second-Order Obstacle Problem of Fractional-order Using Reproducing Kernel Hilbert Space Method

6 Pages Posted: 16 Nov 2018

See all articles by Shatha Hasan

Shatha Hasan

Al-Balqa Applied University

Mohammed Al-Smadi

Al-Balqa Applied University

Asad Freihet

Al-Balqa Applied University

Shaher Momani

University of Jordan

Date Written: July 2018

Abstract

In this paper, reproducing kernel Hilbert space method is employed to approximate the solution and its derivative to second-order boundary-value problems associated with obstacle, unilateral, and contact problems. The analytical solution is represented in the form of a series in the reproducing kernel Hilbert space. The 𝑛-term approximation is obtained and proved to converge to the analytical solution. Moreover, the reproducing kernel Hilbert space method is modified to obtain an approximate solution for the obstacle problem, replacing second derivative by Caputo fractional derivative 𝐷𝑎𝛼,𝛼∈(1,2). A numerical example is given to demonstrate the computation efficiency of the proposed method.

Keywords: Reproducing kernel Hilbert space; Approximate solutions; Boundary-value problems; Caputo derivative.

Suggested Citation

Hasan, Shatha and Al-Smadi, Mohammed and Freihet, Asad and Momani, Shaher, Approximate Solutions of Second-Order Obstacle Problem of Fractional-order Using Reproducing Kernel Hilbert Space Method (July 2018). Proceedings of International Conference on Fractional Differentiation and its Applications (ICFDA) 2018, Available at SSRN: https://ssrn.com/abstract=3285988 or http://dx.doi.org/10.2139/ssrn.3285988

Shatha Hasan (Contact Author)

Al-Balqa Applied University ( email )

PO Box 7064 (19117)
Al-Salt
Amman, 19117
Jordan

Mohammed Al-Smadi

Al-Balqa Applied University ( email )

PO Box 7064 (19117)
Al-Salt
Amman, 19117
Jordan

Asad Freihet

Al-Balqa Applied University ( email )

PO Box 7064 (19117)
Al-Salt
Amman, 19117
Jordan

Shaher Momani

University of Jordan ( email )

Jordan
Amman, Amman 11942
Jordan

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