Erkinjon T. Karimov, Jasurjon S. Akhatov
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
| Jasurjon S. Akhatov |
Physical-Technical Institute, SPA ``Physics-Sun''
Academy of Sciences of Uzbekistan
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