Adomian decomposition method for solving nonlinear fractional sturm-liouville problem

Year 2020, Volume: 41 Issue: 1, 169 - 175, 22.03.2020

Ahu Ercan

https://doi.org/10.17776/csj.632415

Abstract

In the present paper, the Adomian decomposition method is employed for solving nonlinear fractional Sturm-Liouville equation. The numerical results for the eigenfunctions and the eigenvalues are obtained. Also, the present results are demonstrated by the tables and the graphs for different values of considered problem.

Keywords

Nonlinear, Fractional Sturm-Liouville equation, Adomian Decomposition Method, Eigenvalues

References

• [1] Adomian G., A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135 (1988) 501-544.
• [2] Abbaoui K. and Cherruault Y., New ideas for proving convergence of decomposition methods, Comput. Math. Appl., 29(7) (1995) 103-108.
• [3] Adomian G., Stochastic Systems, Academic Press, New York, 1983.
• [4] Adomian G., Nonlinear Stochastic Operator Equations, Academic Press, NewYork, 1986.
• [5] Adomian G., Nonlinear Stochastic Systems Theory and Applications to Physics, Kluwer Academic Publishers, Dordrecht, 1989.
• [6] Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Dordrecht, 1994.
• [7] Al-Mdallal Q. M., An efficient method for solving fractional Sturm-Liouville problems, Chaos Soliton. Fract., 40(1) (2009), 183-189.
• [8] Wazwaz A.M., A new method for solving singular initial value problems in the second-order ordinary differential equations, Appl. Math. Comput., 128(1) (2002), 45-57.
• [9] Somali S. and Gokmen G., Adomian decomposition method for nonlinear Sturm-Liouville problems, Surv. Math. Appl., 2 (2007) 11-20.
• [10] Podlunby I., Fractional Differential Equations, Academic Press, San Diego, CA, USA, 1999.
• [11] Sanchez Cano J.A., Adomian decomposition method for class of nonlinear problems, ISRN Appl. Math., (2011), 1-10.
• [12] Syam M.I., Al-Mdallal Q.M. and Al-Refai M, A numerical method for solving a class of fractional Sturm-Liouville eigenvalues problems, Commun. Numer. Anal., 2017 (2017) 217-232.
• [13] Bas E., Fundamental spectral theory of fractional singular Sturm-Liouville operator, J. Funct. Spaces Appl., (2013) 1-7.
• [14] Bas E. and Metin F., Fractional singular Sturm–Liouville operator for Coulomb potential, Adv. Differ. Equ., 300 (2013) 1-13.
• [15] Bas E., Ozarslan R., Baleanu D. and Ercan A., Comparative simulations for solutions of fractional Sturm-Liouville problems with non-singular operators, Adv. Differ. Equ., 350 (2018) 1-19.
• [16] Yilmazer R. and Bas E., Fractional solutions of confluent hypergeometric equation, J. Chung. Math. Soc., 25(2) (2012).
• [17] Panakhov E. S. and Ercan A., Stability problem of singular Sturm-Liouville equation, TWMS J. Pure Appl. Math., 8(2) (2017), 148-159.
• [18] Ozarslan R., Ercan A. and Bas E., -type fractional Sturm‐Liouville Coulomb operator and applied results, Math. Methods Appl. Sci., (2019) 1-12.
• [19] Wazwaz A.M., Exact solutions to nonlinear diffusion equations obtained by the decomposition method, Appl. Math. Comput., 123(1) (2001), 109-122.
• [20] Bas E. and Ozarslan R., Real world applications of fractional models by Atangana Baleanu fractional derivative, Chaos Soliton. Fract., 116 (2018) 121-125.
• [21] Yucel M., Some methods for approximate solutions of boundary value problems, PhD. Thesis, 2018.