Erkinjon T. Karimov, Jasurjon S. Akhatov
Abstract:
In the present work we investigate the Tricomi problem with an integral
gluing condition for a parabolic-hyperbolic equation involving the Caputo
fractional differential operator. Using the method of energy integrals,
we prove the uniqueness of the solution for the considered problem.
The existence of the solution have been proved applying methods of
ordinary differential equations and Fredholm integral equations.
The solution is represented in an explicit form.
Submitted November 14, 2013. Published January 8, 2014.
Math Subject Classifications: 35M10.
Key Words: Parabolic-hyperbolic equation; Tricomi problem;
Caputo fractional derivative; Green's function.
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Erkinjon T. Karimov Institute of Mathematics National University of Uzbekistan Mirzo Ulugbek, Tashkent, Uzbekistan email: erkinjon@gmail.com |
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Jasurjon S. Akhatov Physical-Technical Institute, SPA ``Physics-Sun'' Academy of Sciences of Uzbekistan Tashkent, Uzbekistan email: jahatov@gmail.com |
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