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Constructing conservation laws for fractional-order integro-differential equations

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Abstract

In a class of functions depending on linear integro-differential fractional-order variables, we prove an analogue of the fundamental operator identity relating the infinitesimal operator of a point transformation group, the Euler–Lagrange differential operator, and Noether operators. Using this identity, we prove fractional-differential analogues of the Noether theorem and its generalizations applicable to equations with fractional-order integrals and derivatives of various types that are Euler–Lagrange equations. In explicit form, we give fractional-differential generalizations of Noether operators that gives an efficient way to construct conservation laws, which we illustrate with three examples.

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Authors and Affiliations

  1. Ufa State Aviation Technical University, Ufa, Russia

    S. Yu. Lukashchuk

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  1. S. Yu. Lukashchuk
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Correspondence to S. Yu. Lukashchuk.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 179–199, August, 2015.

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Lukashchuk, S.Y. Constructing conservation laws for fractional-order integro-differential equations. Theor Math Phys 184, 1049–1066 (2015). https://doi.org/10.1007/s11232-015-0317-8

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  • DOI: https://doi.org/10.1007/s11232-015-0317-8

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