Matrix approach to distributed-order ODEs and PDEs

Basic functions for using matrix approach for distributed-order differential equations, and demos.
Updated 10 May 2012

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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.

Cite As

Igor Podlubny (2024). Matrix approach to distributed-order ODEs and PDEs (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2009a
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Require FEX package

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Version Published Release Notes

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