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References (11)
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M.O. Mamchuev (2013)
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Fundamental solution of a loaded second-order parabolic equation with constant coefficientsDifferential Equations, 51
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M.O. Mamchuev (2015)
Fundamental Solution of a Loaded Second-Order Parabolic Equation with Constant CoefficientsDiffer. Uravn., 51
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M.O. Mamchuev (2010)
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Kraevye zadachi dlya uravnenii i sistem uravnenii s chastnymi proizvodnymi drobnogo poryadka (Boundary Value Problems for Equations and Systems of Equations with Fractional Partial Derivatives) -
M. Mamchuev (2015)
Modified cauchy problem for a loaded second-order parabolic equation with constant coefficientsDifferential Equations, 51
- Publisher
- Springer Journals
- Copyright
- Copyright © 2016 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266116060094
- Publisher site
- See Article on Publisher Site
Abstract
We give well-posed statements of the main initial–boundary value problems in a rectangular domain and in a half-strip for a second-order parabolic equation that contains partial Riemann–Liouville fractional derivatives with respect to one of the two independent variables. We construct Green functions and representations of solutions of these problems. We prove existence and uniqueness theorems for the first boundary value problem and the problem in the half-strip with the boundary condition of the first kind.
Journal
Differential Equations – Springer Journals
Published: Jul 13, 2016