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A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives

Author

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  • Jahanshahi, S.
  • Babolian, E.
  • Torres, D.F.M.
  • Vahidi, A.R.

Abstract

We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving fractional boundary value problems. As an application, we solve a special class of fractional Euler–Lagrange equations. The method is based on Hale and Townsend algorithm for finding the roots and weights of the fractional Gauss–Jacobi quadrature rule and the predictor-corrector method introduced by Diethelm for solving fractional differential equations. Illustrative examples show that the given method is more accurate than the one introduced in [26], which uses the Golub–Welsch algorithm for evaluating fractional directional integrals.

Suggested Citation

  • Jahanshahi, S. & Babolian, E. & Torres, D.F.M. & Vahidi, A.R., 2017. "A fractional Gauss–Jacobi quadrature rule for approximating fractional integrals and derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 295-304.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:295-304
    DOI: 10.1016/j.chaos.2017.04.034
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Odibat, Zaid M., 2009. "Computational algorithms for computing the fractional derivatives of functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2013-2020.
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