Adomian decomposition method for solving nonlinear fractional sturm-liouville problem

Ahu Ercan

doi:10.17776/csj.632415

EN

Adomian decomposition method for solving nonlinear fractional sturm-liouville problem

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.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Ahu Ercan ^*
0000-0001-6290-2155
Türkiye

Publication Date

March 22, 2020

Submission Date

October 12, 2019

Acceptance Date

February 10, 2020

Published in Issue

Year 2020 Volume: 41 Number: 1

DOI

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

IZ

https://izlik.org/JA87CK43BE

APA

Ercan, A. (2020). Adomian decomposition method for solving nonlinear fractional sturm-liouville problem. Cumhuriyet Science Journal, 41(1), 169-175. https://doi.org/10.17776/csj.632415

AMA

1.Ercan A. Adomian decomposition method for solving nonlinear fractional sturm-liouville problem. CSJ. 2020;41(1):169-175. doi:10.17776/csj.632415

Chicago

Ercan, Ahu. 2020. “Adomian Decomposition Method for Solving Nonlinear Fractional Sturm-Liouville Problem”. Cumhuriyet Science Journal 41 (1): 169-75. https://doi.org/10.17776/csj.632415.

EndNote

Ercan A (March 1, 2020) Adomian decomposition method for solving nonlinear fractional sturm-liouville problem. Cumhuriyet Science Journal 41 1 169–175.

IEEE

[1]A. Ercan, “Adomian decomposition method for solving nonlinear fractional sturm-liouville problem”, CSJ, vol. 41, no. 1, pp. 169–175, Mar. 2020, doi: 10.17776/csj.632415.

ISNAD

Ercan, Ahu. “Adomian Decomposition Method for Solving Nonlinear Fractional Sturm-Liouville Problem”. Cumhuriyet Science Journal 41/1 (March 1, 2020): 169-175. https://doi.org/10.17776/csj.632415.

JAMA

1.Ercan A. Adomian decomposition method for solving nonlinear fractional sturm-liouville problem. CSJ. 2020;41:169–175.

MLA

Ercan, Ahu. “Adomian Decomposition Method for Solving Nonlinear Fractional Sturm-Liouville Problem”. Cumhuriyet Science Journal, vol. 41, no. 1, Mar. 2020, pp. 169-75, doi:10.17776/csj.632415.

Vancouver

1.Ahu Ercan. Adomian decomposition method for solving nonlinear fractional sturm-liouville problem. CSJ. 2020 Mar. 1;41(1):169-75. doi:10.17776/csj.632415

Cited By

Construction of the New Wave Solutions of Modified Camassa-Holm and Degasperis-Procesi Equations with Atangana’s Conformable Derivative

Afyon Kocatepe University Journal of Sciences and Engineering

https://doi.org/10.35414/akufemubid.1398202

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December