Geodesic
On arithmetic partial differential equations
Journal of integer sequences, Tome 19 (2016) no. 8
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 
@article{JIS_2016__19_8_a3,
     author = {Haukkanen,  Pentti and Merikoski,  Jorma K. and Tossavainen,  Timo},
     title = {On arithmetic partial differential equations},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {8},
     zbl = {1353.11007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_8_a3/}
}
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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/