Constructing conservation laws for fractional-order integro-differential equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 179-199
Voir la notice de l'article provenant de la source Math-Net.Ru
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.
Keywords:
integro-differential fractional-order equation, symmetry, conservation law, fundamental operator identity, Noether theorem.
@article{TMF_2015_184_2_a0,
author = {S. Yu. Lukashchuk},
title = {Constructing conservation laws for fractional-order integro-differential equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {179--199},
publisher = {mathdoc},
volume = {184},
number = {2},
year = {2015},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a0/}
}
TY - JOUR AU - S. Yu. Lukashchuk TI - Constructing conservation laws for fractional-order integro-differential equations JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2015 SP - 179 EP - 199 VL - 184 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a0/ LA - ru ID - TMF_2015_184_2_a0 ER -
S. Yu. Lukashchuk. Constructing conservation laws for fractional-order integro-differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 184 (2015) no. 2, pp. 179-199. http://geodesic.mathdoc.fr/item/TMF_2015_184_2_a0/