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Mathematics 2015, 3(1), 76-91; doi:10.3390/math3010076

Basic Results for Sequential Caputo Fractional Differential Equations

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA
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Author to whom correspondence should be addressed.
Academic Editor: Hari M. Srivastava
Received: 10 February 2015 / Accepted: 13 March 2015 / Published: 19 March 2015
(This article belongs to the Special Issue Recent Advances in Fractional Calculus and Its Applications)
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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. View Full-Text
Keywords: sequential Caputo fractional derivative; Mittag–Leffler function sequential Caputo fractional derivative; Mittag–Leffler function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sambandham, B.; Vatsala, A.S. Basic Results for Sequential Caputo Fractional Differential Equations. Mathematics 2015, 3, 76-91.

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