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Modified Cauchy problem for a loaded second-order parabolic equation with constant coefficients. (English. Russian original) Zbl 1329.35336
Differ. Equ. 51, No. 9, 1137-1144 (2015); translation from Differ. Uravn. 51, No. 9, 1147-1153 (2015).
Summary: We give a well-posed statement of the initial value problem for a second-order parabolic equation containing Riemann-Liouville fractional partial derivatives in one of the two independent variables. We prove existence and uniqueness theorems for the solution of this problem.

MSC:
35R11 Fractional partial differential equations
35K15 Initial value problems for second-order parabolic equations
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