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Numerical solutions for fractional differential equations by Tau-Collocation method

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  • Allahviranloo, T.
  • Gouyandeh, Z.
  • Armand, A.

Abstract

The main purpose of this paper is to provide an efficient numerical approach for multi-order fractional differential equations based on a Tau-Collocation method. To do this, multi-order fractional differential equations transformed into a system of nonlinear algebraic equations in matrix form. Thus, by solving this system unknown coefficients are obtained. The fractional derivatives are described in the Caputo sense. The rate of convergence for the proposed method is established in the Lwp norm. Some numerical example is also provided to illustrate our results. The results reveal that the method is very effective and simple.

Suggested Citation

  • Allahviranloo, T. & Gouyandeh, Z. & Armand, A., 2015. "Numerical solutions for fractional differential equations by Tau-Collocation method," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 979-990.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:979-990
    DOI: 10.1016/j.amc.2015.09.062
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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. Damarla, Seshu Kumar & Kundu, Madhusree, 2015. "Numerical solution of multi-order fractional differential equations using generalized triangular function operational matrices," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 189-203.
    3. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    4. Hilfer, R., 2003. "On fractional diffusion and continuous time random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 329(1), pages 35-40.
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