Homotopy analysis method for multiple solutions of the fractional Sturm-Liouville problems |
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| Authors: | Saeid Abbasbandy A Shirzadi |
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| Institution: | (1) Theoretical Plasma Physics Division, PINSTECH, P.O. Nilore, Islamabad, 44000, Pakistan;(2) Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad, 44000, Pakistan;(3) Department of Mathematics, COMSATS Institute of Information Technology, H-8, Islamabad, 44000, Pakistan;(4) Department of Mathematics, University of Central Florida, 32816 Orlando, FL, USA |
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| Abstract: | In this paper, Homotopy Analysis Method (HAM) is applied to numerically approximate the eigenvalues of the fractional Sturm-Liouville
problems. The eigenvalues are not unique. These multiple solutions, i.e., eigenvalues, can be calculated by starting the HAM
algorithm with one and the same initial guess and linear operator L\mathcal{L}. It can be seen in this paper that the auxiliary parameter (h/2p),\hbar, which controls the convergence of the HAM approximate series solutions, has another important application. This important
application is predicting and calculating multiple solutions. |
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