Geodesic
On adjoint operators for fractional differentiation operators
Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 131, pp. 284-289

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On a linear manifold of the space of square summable functions on a finite segment vanishing at its ends, we consider the operator of left-sided Caputo fractional differentiation. We prove that the adjoint for it is the operator of right-sided Caputo fractional differentiation. Similar results are established for the Riemann–Liouville fractional differentiation operators. We also demonstrate that the operator, which is represented as the sum of the left-sided and the right-sided fractional differentiation operators is self adjoint. The known properties of the Caputo and Riemann–Liouville fractional derivatives are used to substantiate the results.
Keywords: Caputo fractional derivative, Riemann-Liouville fractional derivative, adjoint operator, square summable function. 
@article{VTAMU_2020_25_131_a3,
     author = {G. Petrosyan},
     title = {On adjoint operators for fractional differentiation operators},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {284--289},
     publisher = {mathdoc},
     volume = {25},
     number = {131},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a3/}
}
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G. Petrosyan. On adjoint operators for fractional differentiation operators. Vestnik rossijskih universitetov. Matematika, Tome 25 (2020) no. 131, pp. 284-289. http://geodesic.mathdoc.fr/item/VTAMU_2020_25_131_a3/