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Kavooci, Zahra, Ghanbari, Kazem, Mirzaei, Hanif. (1402). Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval‎. سامانه مدیریت نشریات علمی, 12(2), 226-235. doi: 10.22034/cmde.2023.54630.2275
Zahra Kavooci; Kazem Ghanbari; Hanif Mirzaei. "Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval‎". سامانه مدیریت نشریات علمی, 12, 2, 1402, 226-235. doi: 10.22034/cmde.2023.54630.2275
Kavooci, Zahra, Ghanbari, Kazem, Mirzaei, Hanif. (1402). 'Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval‎', سامانه مدیریت نشریات علمی, 12(2), pp. 226-235. doi: 10.22034/cmde.2023.54630.2275
Kavooci, Zahra, Ghanbari, Kazem, Mirzaei, Hanif. Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval‎. سامانه مدیریت نشریات علمی, 1402; 12(2): 226-235. doi: 10.22034/cmde.2023.54630.2275

Fractional Chebyshev differential equation on symmetric $\alpha$ dependent interval‎

Computational Methods for Differential Equations
مقاله 3، دوره 12، شماره 2، خرداد 2024، صفحه 226-235    اصل مقاله (361.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.54630.2275
نویسندگان
Zahra Kavooci1؛ Kazem Ghanbari* 1، 2؛ Hanif Mirzaei1
1Faculty of Sciences, Sahand University of Technology, Tabriz, Iran.
2School of Mathematics and Statistics, Carleton University, Ottawa, Canada.
چکیده
Most of fractional differential equations are considered on a fixed interval. In this paper, we consider a typical fractional differential equation on a symmetric interval $[-\alpha,\alpha]$, where $\alpha$ is the order of fractional derivative. For a positive real number α we prove that the solutions are  $T_{n,\alpha}(x)=(\alpha+x)^\frac{1}{2}Q_{n,\alpha}(x)$ where $Q_{n,\alpha}(x)$ produce a family of orthogonal polynomials with respect to the weight function$w_\alpha(x)=(\frac{\alpha+x}{\alpha-x})^{\frac{1}{2}}$ on $[-\alpha,\alpha]$. For integer case $\alpha = 1 $, we show that these polynomials coincide with classical Chebyshev polynomials of the third kind. Orthogonal properties of the solutions lead to practical results in determining solutions of some fractional differential equations. 
کلیدواژه‌ها
Orthogonal polynomials؛ Fractional Chebyshev differential equation؛ Riemann-Liouville and Caputo derivatives
مراجع
  • [1] T. Aboelenen, SA. Bakr, and HM. El-Hawary, Fractional Laguerre spectral methods and their applications to fractional differential equations on unbounded domain, International Journal of Computer Mathematics, 94 (2017), 570–596. doi: 10.1080/00207160.2015.1119270.
  • [2]  M. Abramowitz and A. Stegun, Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, 1970.
  • [3]  M. Ciesielski, M. Klimek, and T. Blaszczyk, The fractional Sturm-Liouville problem-Numerical approximation and application in fractional diffusion, Journal of Computational and Applied Mathematics, 317 (2017), 573–588.
  • [4]  A. Deshpande and V. Daftardar-Gejji, Chaos in discrete fractional difference equations, Pramana – J. Phys., 87 (2016), doi: 10.1007/s12043-016-1231-9.
  • [5]  K. Diethelm, The Analysis of Fractional Differential Equations, Springer-Verlag, Berlin, 2010.
  • [6]  E.H. Doha, W.M. Abd-Elhameed, and M.M. Alsuyuti, On using third and fourth kinds Chebyshev polynomials for solving the integrated formsof high odd-order linear boundary value problems, Journal of the Egyptian Mathematical Society, 23 (2015), 397–405.
  • [7]  M.H. Heydari, M.R. Hooshmandasl, and F.M.M. Ghaini, An efficient computational method for solving fractional biharmonic equation, Computers and Mathematics with Applications, 68 (2014), 269-287.
  • [8]  B. Jin and W. Rundell, An inverse Sturm-Liouville problem with a fractional derivative, Journal of Computational Physics, 231 (2012), 4954–4966.
  • [9]  Z. Kavooci, K. Ghanbari, and H. Mirzaei, New form of Laguerre Fractional Differential Equation and Applications, Turk J Math, 46 (2022), 2998–3010. doi: 10.55730/ 1300-0098.3314.
  • [10]  A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo, Theory and applications of fractional differential equations, NorthHolland mathematics studies, Elsevier science, 204 (2006).
  • [11]  M. Klimek and O.P. Agrawal, Fractional Sturm-Liouville problem, Computers and Mathematics with Applications, 66 (2013), 795–812.
  • [12]  M. Klimek, M. Ciesielski, and T. Blaszczyk, Exact and numerical solutions of the fractional Sturm-Liouville problem, Fractional Calculus and Applied Analysis, 21 (2018), 45–71.
  • [13]  X.T. Liu, H.G. Sun, Y. Zhang, and Z. Fu, A scale-dependent finite difference approximation for time fractional differential equation, Computational Mechanics, 63 (2019), 429–442.
  • [14]  J.C. Mason, Chebyshev polynomials of the second, third and fourth kinds in approximation, indefinite integration, and integral transforms, Journal of Computational and Applied Mathematics, 49 (1993), 169–178.
  • [15]  J.C. Mason and D.C. Handscomb, Chebyshev polynomials, Chapman and Hall, New York, 2003.
  • [16]  I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [17]  A.K. Singh and M. Mehra, Wavelet collocation method based on Legendre polynomials and its application in solving the stochastic fractional integro-differential equations, Journal of Computational science, 51 (2020) 101342, 1–11.
  • [18]  M. Zayernouri and G.E. Karniadakis, Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation , Journal of Computational Physics, 252 (2013), 495–517.
  • [19]  D. Funaro, Polynomial Approximation of Differential Equations, Springer-Verlag, New York, 1991.
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