Bulletin KRASEC. Phys. & Math. Sci. 2017. vol. 16, issue. 1. pp. 17-25. ISSN 2313-0156

DOI: 10.18454/2313-0156-2017-16-1-17-25

MSC 76W05, 86A25

ABOUT A PROBLEM FOR THE DEGENERATING MIXED TYPE EQUATION FRACTIONAL DERIVATIVE

B. I. Islomov¹, N. K. Ochilova²

¹National University of Uzbekistan, 100125, Tashkent, Vuzgorodok, Universitetskaya str.4, Uzbekistan
²Tashkent financial institute,100000, Tashkent, Amir Temur-57.Uzbekistan
E-mail: nargiz.ochilova@gmail.com

The existence and the uniqueness of solution of local problem for degenerating mixed type equation is investigated. Considering parabolic-hyperbolic equation involve the Caputo fractional derivative. The uniqueness of solution is proved using the method of the extremume principle and integral energy, the existence is proved by the method of integral equations.

Keywords: boundary value problem, degenerating equation, parabolic-hyperbolic type, Gauss hypergeometric function, Cauchy problem, existence and uniqueness of solution, a principle an extremum, method of integral equations, Caputo fractional derivative.

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For citation: Islomov B. I., Ochilova N. K. About a problem for the degenerating mixed type equation fractional derivative. Bulletin KRASEC. Physical and Mathematical Sciences 2017, vol.16, issue 1, 17-25. DOI: 10.18454/2313-0156-2017-16-1-17-25

Original article submitted: 25.12.2016

islomov

   

 

     Islamov  Bozor  – Dr. Si. (Phys & Math), Professor, Department of Differential equations and mathematical physics, National University of Uzbekistan named by Mirzo Ulugbek, Tashkent, Rep  ublic of Uzbekistan.

   

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Ochilova

 

    Ochilova Nargiza Komilovna — assistant professor of mathematical analysis of physical and mathematical fakultetaTashkenskogo Pedagogical University. Nizami, Tashkent, Republic of Uzbekistan.

 

     

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