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Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations

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  • Yongjin Li
  • Kamal Shah

Abstract

We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.

Suggested Citation

  • Yongjin Li & Kamal Shah, 2017. "Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2017(1).
    • Handle: RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:1535826
    DOI: 10.1155/2017/1535826
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    References listed on IDEAS

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    1. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
    2. Shah, Kamal & Khalil, Hammad & Khan, Rahmat Ali, 2015. "Investigation of positive solution to a coupled system of impulsive boundary value problems for nonlinear fractional order differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 240-246.
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