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Matrix approach to distributed-order ODEs and PDEs


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Matrix approach to distributed-order ODEs and PDEs



07 May 2012 (Updated )

Basic functions for using matrix approach for distributed-order differential equations, and demos.

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This submission contains the basic functions that are necessary for using the matrix approach to discretization of distributed-order differential equations, and demos.
It provides the Matlab code from Appendices 4-6 to the following book:
[1] Zh. Jiao, YQ. Chen, I. Podlubny: "Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives", Springer, London, 2012, ISBN 978-1-4471-2851-9, (

The code from Appendices 1-3 can be found in FEX submission #36574 "Demos for investigating distributed-order linear time-invariant systems" by Zhuang Jiao (

The matrix approach for differential equations with fractional-order derivatives in the case of constant orders of derivatives is described in the following articles:
[2] I. Podlubny, "Matrix approach to discrete fractional calculus", Fractional Calculus and Applied Analysis, vol. 3, no. 4, 2000, pp. 359-386 ( ).
[3] I. Podlubny, A. Chechkin, T. Skovranek, YQ. Chen, B. M. Vinagre Jara, "Matrix approach to discrete fractional calculus II: partial fractional differential equations", Journal of Computational Physics, vol. 228, no. 8, 1 May 2009, pp. 3137-3153, (preprint: )
For more information about fractional differential equations (i.e., differential equations containing derivatives of arbitrary real order) see, for example,
[4] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999, ISBN 0125588402.


Require Fex Package inspired this file.

MATLAB release MATLAB 7.8 (R2009a)
Other requirements This function needs access to the internet for downloading required/suggested packages from the File Exchange.
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Comments and Ratings (1)
13 Oct 2012 farhaad fakhravar


10 May 2012

Updated description. Added a references to the related FEX submission #36574, and an option to download and install it.

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