A novel operational matrix for the numerical solution of nonlinear Lane–Emden system of fractional order

• Abd-Elhameed WM, Doha EH, Youssri YH, Bassuony MA (2016) New Tchebyshev-Galerkin operational matrix method for solving linear and nonlinear hyperbolic telegraph type equations. Numer Methods Partial Differ Equ 36(6):1553–1571

  Article  MathSciNet  Google Scholar 

• Ameen IG, Zaky MA, Doha EH (2021) Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative. J Comput Appl Math 392:113468

• Babolian E, Eftekhari A, Saadatmandi A (2015) A Sinc-Galerkin technique for the numerical solution of a class of singular boundary value problems. J Comput Appl Math 34:45–63

  MathSciNet  MATH  Google Scholar 

• Bhrawy AH, Taha TM, Machado JAT (2015) A review of operational matrices and spectral techniques for fractional calculus. Nonlinear Dyn 81:1023–1052

  Article  MathSciNet  Google Scholar 

• D. Dominici, Orthogonality of the Dickson polynomials of the \((k + 1)\)-th kind. Johannes Kepler University Linz, Doktoratskolleg “Computational Mathematics”, Altenberger Straße 69, 4040 Linz, Austria (2017)

• Flockerzi D, Sundmacher K (2011) On coupled Lane–Emden equations arising in dusty fluid models. J Phys 268:012006

  Google Scholar 

• Gürbüz B, Sezer M (2017) Laguerre polynomial solutions of a class of initial and boundary value problems arising in science and engineering fields. Acta Phys Pol A 132(3):558–560

  Article  Google Scholar 

• Hao TC, Cong FZ, Shang YF (2018) An efficient method for solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions and error estimate. J Math Chem 56:2691–2706

  Article  MathSciNet  Google Scholar 

• Irfan N, Kumar S, Kapoor S (2014) Bernstein operational matrix approach for integro-differential equation arising in control theory. Nonlinear Eng Model Appl 3(2):117–123

  Google Scholar 

• Kilbas AA, Srivastava HM, Trujillo JJ (2006) Theory and applications of fractional differential equations. Elsevier, San Diego

  MATH  Google Scholar 

• Kürkçü ÖK, Aslan E, Sezer M, İlhan O (2016) A numerical approach technique for solving generalized delay integro-differential equations with functional bounds by means of Dickson polynomials. Int J Comput Methods 36(6):18500239

  MATH  Google Scholar 

• Muatjetjeja B, Khalique CM (2010) Noether, partial noether operators and first integrals for the coupled Lane–Emden system. Math Comput Appl 15:325–333

  MathSciNet  MATH  Google Scholar 

• Nagy AM, Sweilam NH, El-Sayed AA (2018) New operational matrix for solving multi-term variable order fractional differential equations. J Comput Nonlinear Dyn 13:011001–011007

  Article  Google Scholar 

• Nagy AM, El-Sayed AA (2019) An accurate numerical technique for solving two-dimensional time fractional order diffusion equation. Int J Model Simul 39(3):214–221

  Article  Google Scholar 

• Narasimhan R (1985) Analysis on real and complex manifolds. North-Holland Mathematical Library, 35. North-Holland Publishing Co., Amsterdam

• Naik PA, Zu J, Owolabi KM (2020) Modelling the mechanics of viral kinetics under immune control during primary infection of HIV-1 with treatment in fractional order. Physica A 545(1):123816

  Article  MathSciNet  Google Scholar 

• Odibat Z, Momani S (2009) The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics. Comput Math Appl 58:2199–2208

  Article  MathSciNet  Google Scholar 

• Öztürk Y, Gülsu M (2017) Numerical solution of Abel equation using operational matrix method with Chebyshev polynomials. Asian-Eur J Math 10(3):1750053

  Article  MathSciNet  Google Scholar 

• Öztürk Y (2019) An efficient numerical algorithm for solving system of Lane-Emden type equations arising in engineering. Nonlinear Eng 8:429–437

  Article  Google Scholar 

• Parand K, Pirkhedri A (2010) Sinc-collocation method for solving astrophysics equations. New Astron 15:533–573

  Article  Google Scholar 

• Parand K, Dehghan M, Rezaei AR, Ghaderi S (2010) An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method. Comput Phys Commun 181:1096–1108

  Article  MathSciNet  Google Scholar 

• Pinto CMA, Carvalho ARM (2015) Fractional modeling of typical stages in HIV epidemics with drug-resistance. Prog Fract Differ Appl 1(2):111–122

  Google Scholar 

• Qureshi S, Yusuf A (2019) Modeling chickenpox disease with fractional derivatives: from caputo to atangana-baleanu. Chaos Solitons Fractals 122:111–118

  Article  MathSciNet  Google Scholar 

• Rach R, Duan JS, Wazwaz AM (2014) Solving coupled Lane–Emden boundary value problems in catalytic diffusion reactions by the adomian decomposition method. J Math Chem 52:255–267

  Article  MathSciNet  Google Scholar 

• Sweilam NH, Nagy AM, El-Sayed AA (2016) Numerical approach for solving space fractional order diffusion equations using shifted Chebyshev polynomials of the fourth kind. Turk J Math 40:1283–1297

  Article  MathSciNet  Google Scholar 

• Sun HG, Zhang Y, Baleanu D, Chen W, Chen YQ (2018) A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlinear Sci Numer Simul 64:213–231

  Article  Google Scholar 

• Wang Q, Yucas JL (2012) Dickson polynomials over finite fields. Finite Fields Appl 18(4):814–831

  Article  MathSciNet  Google Scholar 

• Wazwaz AM, Rach R, Duan J-S (2013) A study on the systems of the Volterra integral forms of the Lane–Emden equations by the Adomian decomposition method. Math Methods Appl Sci 37(1):10–19

  Article  MathSciNet  Google Scholar 

• Zaky MA, Ameen IG, Abdelkawy MA (2017) A new operational matrix based on Jacobi wavelets for a class of variable-order fractional differential equations. Proc Roman Acad Ser A Math Phys Tech Sci Inf Sci 18(4):315–322

  MathSciNet  Google Scholar 

• Zaky MA (2019) Recovery of high order accuracy in Jacobi spectral collocation methods for fractional terminal value problems with non-smooth solutions. J Comput Appl Math 357:103–122

  Article  MathSciNet  Google Scholar 

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