Basic Results for Sequential Caputo Fractional Differential Equations

Bhuvaneswari Sambandham and Aghalaya S. Vatsala
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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

Mathematics, 2015, vol. 3, issue 1, 1-16

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.

Keywords: sequential Caputo fractional derivative; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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