Geodesic
On arithmetic partial differential equations
Journal of integer sequences, Tome 19 (2016) no. 8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Kovič, and implicitly Ufnarovski and Åhlander, defined a notion of arithmetic partial derivative. We generalize the definition for rational numbers and study several arithmetic partial differential equations of the first and second order. For some equations, we give a complete solution, and for others, we extend previously known results. For example, we determine under which conditions two consecutive partial derivations are commutative.
Classification : 11A25, 11A51
Keywords: arithmetic derivative, partial derivative 
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     title = {On arithmetic partial differential equations},
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Haukkanen, Pentti; Merikoski, Jorma K.; Tossavainen, Timo. On arithmetic partial differential equations. Journal of integer sequences, Tome 19 (2016) no. 8. http://geodesic.mathdoc.fr/item/JIS_2016__19_8_a3/