Solvability of BVPs for the parabolic-hyperbolic equation with non-linear loaded term

Obidjon Kh. Abdullaev<sup>ab

a</sup> Romanovsky Institute of Mathematics, Tashkent, Uzbekistan
^b National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: This work is devoted to prove the existence and uniqueness of solution of BVP with non-local assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation involving Caputo derivatives. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of integral equations.

Keywords: Caputo fractional derivatives, loaded equation, integral gluing condition, non-linear integral equation, non-local problem, existence and uniqueness of solution.

UDC: 517.956

Received: 10.09.2020
Received in revised form: 10.11.2020
Accepted: 20.02.2021

Language: English

DOI: 10.17516/1997-1397-2021-14-2-133-143

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