Geodesic
Inverting of generalized Riemann–Liouville operator by means of integral Laplace transform
Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 41-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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We employ the integral Laplace transform to invert the generalized Riemann–Liouville operator in a closed form. We establish that the inverse generalized Riemann–Liouville operator is a differential or integral-differential operator. We establish a relation between Riemann–Liouville operator and Temlyakov–Bavrin operator. We provide new examples of generalized Riemann–Liouville operator.
Keywords: Riemann–Liouville operator, fractional integral
Mots-clés : Laplace transform. 
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I. I. Bavrin; O. E. Iaremko. Inverting of generalized Riemann–Liouville operator by means of integral Laplace transform. Ufa mathematical journal, Tome 8 (2016) no. 3, pp. 41-48. http://geodesic.mathdoc.fr/item/UFA_2016_8_3_a4/

[1] Bavrin I. I., Operatornyi metod v kompleksnom analize, Prometei, M., 1988, 200 pp. | MR

[2] Bavrin I. I., Matrosov V. L., Yaremko O. E., Integralnye preobrazovaniya i predstavleniya funktsii v deistvitelnoi i kompleksnoi oblastyakh, Prometei, M., 2000, 416 pp.

[3] Berdyshev A. S., Turmetov B. Kh., Kadirkulov B. Zh., “Nekotorye svoistva i primeneniya integrodifferentsialnykh operatorov tipa Adamara–Marsho v klasse garmonicheskikh funktsii”, Sib. mat. zhurnal, 53:4 (2012), 752–764 | MR | Zbl

[4] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, v. 1, Nauka, M., 1973, 295 pp. | MR

[5] Dzhrbashyan M. M., “Obobschennyi operator Rimana–Liuvillya i nekotorye ego primeneniya”, Izv. AN SSSR. Ser. matem., 32:5 (1968), 1075–1111 | MR | Zbl

[6] Dzhrbashyan M. M., Nersesyan A. B., “Drobnye proizvodnye i zadacha Koshi dlya differentsialnykh uravnenii drobnogo poryadka”, Izvestiya AN Armyanskoi SSR. Ser. Matematika, 3:1 (1968), 3–29 | Zbl

[7] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003, 272 pp.

[8] Nakhushev A. M., Uravneniya matematicheskoi biologii, Vysshaya shkola, M., 1995, 301 pp.

[9] Potapov A. A., “Kratkoe istoricheskoe esse o zarozhdenii i stanovlenii teorii drobnogo integrodifferentsirovaniya”, Nelineinyi mir, 1:1–2 (2003), 69–81

[10] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka, Nauka i tekhnika, Minsk, 1987, 687 pp. | MR

[11] Uchaikin V. V., Metod drobnykh proizvodnykh, Artishok, Ulyanovsk, 2008, 512 pp.

[12] Khille E., Fillips R., Funktsionalnyi analiz i polugruppy, Inostrannaya literatura, M., 1962, 830 pp. | MR

[13] Churikov V. A., “Drobnyi analiz na osnove operatora Adamara”, Izvestiya Tomskogo politekhnicheskogo universiteta, 312:2, Matematika i mekhanika. Fizika (2008), 16–20

[14] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 2, Mir, M., 1984

[15] A. A. Kilbas, H. M. Srivastava., J. J. Trujillo, Theory and Applications of Fractional Differential Equations, Mathematics Studies, 204, Elsevier, 2006 | MR | Zbl

[16] A. N. Kochubei, Distributed Order Derivatives and Relaxation Patterns, 2009/5/5, arXiv: 0905.0616 | MR

[17] A. N. Kochubei, “Distributed order calculus and equations of ultraslow diffusion”, Journal of Mathematical Analysis and Applications, 340:1 (2008), 251–282 | DOI | MR

[18] A. N. Kochubei, “General fractional calculus, evolution equations, and renewal processes”, Integral Equations and Operator Theory, 71:4 (2011), 583–600 | DOI | MR | Zbl