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A Shifted Jacobi‐Gauss Collocation Scheme for Solving Fractional Neutral Functional‐Differential Equations

Author

Listed:
  • A. H. Bhrawy
  • M. A. Alghamdi

Abstract

The shifted Jacobi‐Gauss collocation (SJGC) scheme is proposed and implemented to solve the fractional neutral functional‐differential equations with proportional delays. The technique we have proposed is based upon shifted Jacobi polynomials with the Gauss quadrature integration technique. The main advantage of the shifted Jacobi‐Gauss scheme is to reduce solving the generalized fractional neutral functional‐differential equations to a system of algebraic equations in the unknown expansion. Reasonable numerical results are achieved by choosing few shifted Jacobi‐Gauss collocation nodes. Numerical results demonstrate the accuracy, and versatility of the proposed algorithm.

Suggested Citation

  • A. H. Bhrawy & M. A. Alghamdi, 2014. "A Shifted Jacobi‐Gauss Collocation Scheme for Solving Fractional Neutral Functional‐Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlamp:v:2014:y:2014:i:1:n:595848
    DOI: 10.1155/2014/595848
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    References listed on IDEAS

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    1. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. D. Baleanu & A. H. Bhrawy & T. M. Taha, 2013. "Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, June.
    3. Fei Gao & Xue-Jing Lee & Heng-qing Tong & Feng-xia Fei & Hua-ling Zhao, 2013. "Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional‐Order Chaotic Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. A. H. Bhrawy, 2013. "A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, November.
    5. Fei Gao & Xue-Jing Lee & Heng-qing Tong & Feng-xia Fei & Hua-ling Zhao, 2013. "Identification of Unknown Parameters and Orders via Cuckoo Search Oriented Statistically by Differential Evolution for Noncommensurate Fractional-Order Chaotic Systems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, December.
    6. A. H. Bhrawy, 2013. "A New Numerical Algorithm for Solving a Class of Fractional Advection‐Dispersion Equation with Variable Coefficients Using Jacobi Polynomials," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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