Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 12. no. 1. pp. 5-11. ISSN 2313-0156

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DOI: 10.18454/2313-0156-2016-12-1-5-11

MATHEMATICS

MSC 35M10

ON A PROBLEM FOR THE LOADED MIXED TYPE EQUATION WITH FRACTIONAL DERIVATIVE

O.Kh. Abdullayev

National University of Uzbekistan by Mirzo Ulugbeka, 100174, Uzbekistan, Tashkent c., VUZ gorodok st.
E-mail: obidjon.mth@gmail.com

An existence and an uniqueness of solution of local boundary value problem with discontinuous matching condition for the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals have been investigated in this research work. The uniqueness of solution is proved by the method of integral energy and the existence is proved by the method of integral equations.

Key words: Caputo derivative, boundary value problem, Riemann-Liouville integral, energy integral.

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For citation: Abdullayev O.Kh. On a problem for the loaded mixed type equation with fractional derivative. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 12, no 1, 5-11. DOI: 10.18454/2313-0156-2016-12-1-5-11

Original article submitted: 20.03.2016

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Abdulaev

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Abdullayev Obidjon Khayrullaevich – Ph.D. (Phys. & Math.), Associate Professor Dept. of Differential equations of the National University of Uzbekistan named after Ulugbek, Uzbekistan.

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