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Mixed problem for a system of fractional partial differential equations. (English. Russian original) Zbl 1338.35474
Differ. Equ. 52, No. 1, 133-138 (2016); translation from Differ. Uravn. 52, No. 1, 132-136 (2016).
Summary: We study a mixed boundary value problem in the general setting for a system of Riemann-Liouville fractional partial differential equations with constant matrix coefficients. By using a system of Volterra integral equations of the second kind, we reduce the problem to a special case for which the solution was earlier constructed in terms of the Green matrix. Existence and uniqueness theorems are proved for the problem in question.

35R11 Fractional partial differential equations
Full Text: DOI
[1] Nakhushev, A.M., Drobnoe ischislenie i ego primenenie (Fractional Calculus and Its Applications), Moscow, 2003. · Zbl 1066.26005
[2] Mamchuev, M.O., Fundamental solution of a system of fractional partial differential equation, Differ. Uravn., 46, 1113-1124, (2010) · Zbl 1385.76012
[3] Mamchuev, M.O., Boundary value problems for a system of fractional partial differential equations in unbounded domains, Dokl. Adygsk. (Cherkessk.) Mezhdunar. Akad. Nauk, 7, 60-63, (2003)
[4] Mamchuev, M.O., Cauchy problem in nonlocal statement for a system of fractional partial differential equations, Differ. Uravn., 48, 351-358, (2012) · Zbl 1273.35298
[5] Mamchuev, M.O., Amixed problem for aweighted system of equations with Riemann-Liouville derivatives, Mat. Zametki, 97, 428-439, (2015)
[6] Heibig, A., Existence of solutions for a fractional derivative system of equations, Integral Equations Operator Theory, 72, 483-508, (2012) · Zbl 1273.35294
[7] Kochubei, A.N., Fractional-parabolic systems, Potential Anal., 37, 1-30, (2012) · Zbl 1259.35218
[8] Kochubei, A.N., Fractional-hyperbolic systems, Fract. Calc. Appl. Anal., 16, 860-873, (2013) · Zbl 1312.35183
[9] Pskhu, A.V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka (Fractional Partial Differential Equations), Moscow: Nauka, 2005. · Zbl 1193.35245
[10] Marichev, O.I., Metody vychisleniya integralov ot spetsial’nykh funktsii (A Method for Calculating Integrals of Special Functions), Moscow: Nauka, 1978. · Zbl 0473.33001
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