Geodesic
Solution in explicit form of non-local problem for differential equation with partial fractional derivative of Riemann--Liouville
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 151-157.

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A non-local problem for a mixed type equation with partial fractional derivative of Riemann–Liouville is studied, boundary condition of which contains generalized operator of fractional integro-differentiation. Unique solution of the problem is then proved.
Keywords: boundary-value problem, fractional derivatives and integrals, fractional differential equation, Mittag–Leffler function. 
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S. A. Sayganova. Solution in explicit form of non-local problem for differential equation with partial fractional derivative of Riemann--Liouville. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 151-157. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a19/

[1] Samko S. G., Kilbas A. A., Marichev O. I., Integrals and derivatives of fractional order and some of their applications, Nauka i Tekhnika, Minsk, 688 pp. | MR | Zbl

[2] Kilbas A. A., Repin O. A., “An analog of the Tricomi problem for a mixed type equation with a partional fractional derivative”, Fract. Calc. Appl. Anal., 13:2 (2010), 69–84 | MR | Zbl

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

[4] Pskhu A. V., Partial differential equations of fractional order, Nauka, Moskva, 2005, 199 pp. | MR | Zbl

[5] Gekkieva S. Kh., “A boundary value problem for the generalized transport equation with fractional derivative in the semi-infinite domains”, Izv. Kabar.-Balkar. nauchn. tsentra RAN, 2002, no. 1(8), 6–8

[6] 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 | Zbl

[7] Repin O. A., Shuvalova T. V., “Nonlocal boundary value problem for an equation of the mixed type with two degeneration lines”, Differ. Equ., 44:6 (2008), 876–880 | DOI | MR | Zbl

[8] Nakhusheva V. A., Differential equations of mathematical models of nonlocal processes, Nauka, Moskva, 2006, 173 pp. | MR | Zbl

[9] Kilbas A. A., Saigo M., “On Mittag–Leffler type function and applications”, Integral Transform. Spec. Funct., 7:1–2 (1998), 97–112 | MR | Zbl

[10] Kilbas A. A., Saigo M., “On solution of integral equation of Abel–Volterra type”, Differ. Integral Equ., 8:5 (1995), 993–1011 | MR | Zbl

[11] Djrbashian M. M., Integral transforms and representations of functions in the complex domain, Nauka, Moskva, 1966, 672 pp.