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Basic Results for Sequential Caputo Fractional Differential Equations

Author

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  • Bhuvaneswari Sambandham

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

  • Aghalaya S. Vatsala

    (Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

Abstract

We have developed a representation form for the linear fractional differential equation of order q when 0 < q < 1 , with variable coefficients. We have also obtained a closed form of the solution for sequential Caputo fractional differential equation of order 2q , with initial and boundary conditions, for 0 < 2q < 1 . The solutions are in terms of Mittag–Leffler functions of order q only. Our results yield the known results of integer order when q = 1 . We have also presented some numerical results to bring the salient features of sequential fractional differential equations.

Suggested Citation

  • Bhuvaneswari Sambandham & Aghalaya S. Vatsala, 2015. "Basic Results for Sequential Caputo Fractional Differential Equations," Mathematics, MDPI, vol. 3(1), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:1:p:76-91:d:47060
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    References listed on IDEAS

    as
    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    2. Jagdev Singh & Devendra Kumar & Adem Kılıçman, 2014. "Numerical Solutions of Nonlinear Fractional Partial Differential Equations Arising in Spatial Diffusion of Biological Populations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, August.
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