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ЖУРНАЛЫ // Журнал Сибирского федерального университета. Серия «Математика и физика»

Журн. СФУ. Сер. Матем. и физ., 2023, том 16, выпуск 3, страницы 357–369 (Mi jsfu1085)

Boubaker operational matrix method for fractional Emden–Fowler problem
Abdelkrim Bencheikh, Lakhdar Chiter

Список литературы

1. S.Abbas, Gh.Azam, E.Ali, “Numerical study of singular fractional Lane-Emden type equations arising in astrophysics”, J. Astrophys. Astr., 40:27 (2019), 2–12  crossref
2. A.Bencheikh, L.Chiter, H.Abbassi, “Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems”, J. Math. Computer Sci., 17:1 (2017), 66–75  crossref  zmath
3. K.Boubaker, “On modified Boubaker polynomials: some differential and analytical properties of the new polynomials issued from an attempt for solving Bi-varied heat equation”, Trends Appl. Sci. Res., 2:6 (2007), 540–544  crossref  mathscinet
4. K.Boubaker, “The Boubaker polynomials, a new function class for solving Bi-varied second order differential equations”, Far East J. Appl. Math., 31:3 (2008), 299–320  mathscinet  zmath
5. A.Bolandtalat, E.Babolian, H.Jafari, “Numerical solutions of multi-order fractional differential equations by Boubaker Polynomials”, Open Phys., 14:1 (2016), 226–230  crossref
6. B.Caruntu, C.Bota, L.Marioara, M.Pasca, “Polynomial Least Squares Method for Fractional Lane-Emden Equations”, Symmetry, 11:4 (2019), 479  crossref  zmath
7. S.Chandrasekhar, An introduction to the study of stellar structure, Dover Publications, Inc, New York, 1967  mathscinet
8. M.S.H.Chowdhury, I.Hashim, “Solutions of Emden-Fowler equations by homotopy-perturbation method”, Nonlinear Anal. Real World Appl., 10:1 (2009), 104–115  crossref  mathscinet  zmath
9. S. Das, Functional Fractional Calculus, Springer, 2011  mathscinet  zmath
10. K.Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer, 2010  mathscinet  zmath
11. S.Davaeifar, J.Rashidinia, “Boubaker polynomials collocation approach for solving systems of nonlinear Volterra-Fredholm integral equations”, Journal of Taibah University for Science, 11:6 (2017), 1182–1199  crossref
12. H.Huan Wang, Y.Hu, “Solutions of fractional Emden-Fowler equations by homotopy analysis method”, Journal of Advances in Mathematics, 13:1 (2017), 1–6  crossref
13. A.K.Nasab, Z.P.Atabakan, A.I.Ismail, W.I.Rabha, “A numerical method for solving singular fractional Lane-Emden type equations”, Journal of King Saud University-Science, 30:1 (2018), 120–130  crossref
14. A.A.Kilbas, H.M.Srivastava, J.J.Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006  mathscinet  zmath
15. E.Kreyszig, Introductory Functional Analysis with Applications, Wiley, New York, 1987  mathscinet
16. H.Labiadh, K.Boubaker, “A Sturm-Liouville shaped characteristic differential equation as a guide to establish a quasi-polynomial expression to the Boubaker polynomials”, Diff. Eq. Cont. Proc., 2:2 (2007), 117–133  mathscinet  zmath
17. I.Podlubny, Fractional Differential Equations, Academic Press, New York, 1999  mathscinet  zmath
18. J.Rebenda, Z.Smarda, “A Numerical Approach for Solving of Fractional Emden-Fowler Type Equations”, AIP Conference Proceedings, 1978:1 (2018), 140006  crossref
19. K.Rabiei, Y.Ordokhani, E.Babolian, “The Boubaker polynomials and their application to solve fractional optimal control problems”, Nonlinear Dyn. Nonlinear Dynamics, 88:2 (2017), 1013–1026  crossref  mathscinet  zmath
20. M.I Syam, “Analytical Solution of the Fractional Initial Emden-Fowler Equation Using the Fractional Residual Power Series Method”, Int. J. Appl. Comput. Math., 4:106 (2018), 02–08  mathscinet
21. M.I.Syam et al., “An accurate method for solving a singular second-order fractional Emden-Fowler problem”, Advances in Difference Equations, 2018, no. 30, 02–16  mathscinet
22. N.T.Shawagfeh, “Analytical approximate solutions for nonlinear fractional differential equations”, Appl. Math. Comput., 131:2-3 (2002), 517–529  mathscinet  zmath
23. P.K.Sahu, B.Mallick, “Approximate Solution of Fractional Order Lane-Emden Type Differential Equation by Orthonormal Bernoulli's Polynomials”, Int. J. Appl. Comput. Math., 5:3 (2019), 89  crossref  mathscinet  zmath
24. X.F.Shang, P.Wu, X.P.Shao, “An efficient method for solving Emden-Fowler equations”, J. Franklin Inst., 346:9 (2009), 889–897  crossref  mathscinet  zmath
25. N.Tripathi, “Shifted Legendre Operational Matrix for Solving Fractional Order Lane-Emden Equation”, National Academy Science Letters, 42:2 (2019), 139–145  crossref  mathscinet
26. A.M.Wazwaz, “Adomian decomposition method for a reliable treatment of the Emden-Fowler equation”, Appl. Math. Comput., 161:2 (2005), 543–560  mathscinet  zmath
27. A.M.Wazwaz, “Analytical solution for the time-dependent Emden-Fowler type of equations by Adomian decomposition method”, Appl. Math. Comput., 166:3 (2005), 638–651  mathscinet  zmath
28. S.A.Yousefi, “Legendre scaling function for solving generalized Emden-Fowler equations”, J. Inf. Syst. Sci., 3:2 (2007), 243–250  mathscinet  zmath


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