Geodesic
On nonlocal problem with fractional Riemann--Liouville derivatives
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 1, pp. 112-121.

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The unique solvability is investigated for the problem of equation with partial fractional derivative of Riemann–Liouville and boundary condition that contains the generalized operator of fractional integro-differentiation. The uniqueness theorem for the solution of the problem is proved on the basis of the principle of optimality for a nonlocal parabolic equation and the principle of extremum for the operators of fractional differentiation in the sense of Riemann–Liouville. The proof of the existence of solutions is equivalent to the problem of solvability of differential equations of fractional order. The solution is obtained in explicit form.
Keywords: boundary value problem, generalized fractional integro-differentiation operator, Gauss hypergeometric function, fractional differential equation. 
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A. V. Tarasenko; I. P. Egorova. On nonlocal problem with fractional Riemann--Liouville derivatives. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 1, pp. 112-121. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_1_a5/

[1] Samko St. G., Kilbas A. A., Marichev O. I., Fractional integrals and derivatives: theory and applications, Gordon and Breach, New York, NY, 1993, xxxvi+976 pp. | MR | MR | Zbl

[2] Saigo M., “A remark on integral operators involving the Gauss hypergeometric function”, Math. Rep. Coll. Gen. Educ., Kyushu Univ., 11:2 (1978), 135–143 | MR | Zbl

[3] Kilbas A. A., Repin O. A., “An Analog of the Bitsadze–Samarskii Problem for a Mixed Type Equation with a Fractional Derivative”, Differ. Equ., 39:5 (2003), 674–680 | DOI | MR | MR | Zbl

[4] Gekkieva S. Kh., “An analog of the Tricomi problem for a mixed type equation with a partial fractional derivative”, Izvestiya Kabardino-Balkarskaya Nauchnoogo Tsentra RAN, 2001, no. 2(7), 78–80 (In Russian)

[5] Kilbas A. A., Repin O. A., “Analog of the Tricomi problem for differential equations with partial derivatives containing fractional diffusion equation”, Dokl. AMAN, 12:1 (2010), 31–39 (In Russian) | MR

[6] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka [Partial Differential Equations of Fractional Order], Nauka, Moscow, 2005, 199 pp. (In Russian) | MR

[7] Smirnov M. M., Vyrozhdaiushchiesia ellipticheskie i giperbolicheskie uravneniia [Degenerate Elliptic and Hyperbolic Equation], Nauka, Moscow, 1966, 292 pp. (In Russian) | MR

[8] Nakhushev A. M., Drobnoe ischislenie ego primenenie [Fractional Calculation and its Application], Fizmatlit, Moscow, 2009, 272 pp. (In Russian)

[9] Nakhusheva V. A., Differentsial'nye uravneniia matematicheskikh modelei nelokal'nykh protsessov [Differential Equations of Mathematical Models of Non-Local Processes], Nauka, Moscow, 2006, 173 pp. (In Russian) | MR