Geodesic
On the fundamental solution of an ordinary
News of the Kabardin-Balkar scientific center of RAS, no. 6-1 (2018), pp. 48-52.

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In this paper, we study an ordinary differential equation with a continuous distributed differentiation operator. Fractional differentiation is understood in the sense of Riemann–Liouville. For the equation under consideration, a fundamental solution is constructed and the Cauchy problem is written in explicit form.
Keywords: fundamental solution, Cauchy problem, continuous distributed differentiation operator, Riemann–Liouville fractional differentiation operator. 
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B. I. Efendiev. On the fundamental solution of an ordinary. News of the Kabardin-Balkar scientific center of RAS, no. 6-1 (2018), pp. 48-52. http://geodesic.mathdoc.fr/item/IZKAB_2018_6-1_a7/

[1] A. M. Nakhushev, “O nepreryvnykh differentsialnykh uravneniyakh i ikh raznostnykh analogakh”, Dokl. AN SSSR, 300:4 (1988), 796–799 | MR | Zbl

[2] A. M. Nakhushev, “O polozhitelnosti operatorov nepreryvnogo i diskretnogo differentsirovaniya i integrirovaniya vesma vazhnykh v drobnom ischislenii i v teorii uravnenii smeshannogo tipa”, Differents. uravneniya, 34:1 (1998), 101–109 | MR | Zbl

[3] A. M. Nakhushev, Uravneniya matematicheskoi biologii dlya universitetov, ucheb. posobie, Vysshaya shkola., M., 1995, 301 pp.

[4] V. Volterra, Teoriya funktsionalov integralnykh i integro-differentsialnykh uravnenii, Nauka, M., 1982

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

[6] A. V. Pskhu, Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005, 199 pp.

[7] A. N. Kochubei, “Distributed order calculus and equations of ultraslow diffusion”, J. Math. Anal. Appl, 340 (2008), 252–281 | DOI | MR | Zbl

[8] Yu. Luchko, “Boundary value problems for the generalized time-fractional diffusion equation of distributed order”, Fract. Calc. Appl. Anal, 12 (2009), 409–422 | MR | Zbl

[9] A. V. Pskhu, “Fundamentalnoe reshenie obyknovennogo differentsialnogo uravneniya kontinualnogo poryadka”, Dokl. Adygskoi (Cherkesskoi) Mezhdunarodnoi akademii nauk, 9:1 (2007), 73–78