In this work, we present the advanced fractional model described with the loaded parabolic–hyperbolic‐type equation. Also, for this equation, we investigate a Cauchy‐type problem with a line of changing type. The existence and uniqueness of the solutions to the problem are proven using the theory of integral equations.
This work devoted to prove of uniqueness and existence of solution of the nonlocal problem with integral gluing condition for the loaded parabolic‐hyperbolic type equation involving Caputo derivatives which loaded parts in Riemann‐Liouville integral‐differential operator. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method...
The purpose of this paper is to establish unique solvability for a certain generalized boundary‐value problem for a loaded third‐order integro‐differential equation with variable coefficients. Moreover, the method of integral equations is applied to obtain an equation related to the Riemann‐Liouville operators.
This research work is devoted to investigations of the existence and uniqueness of the solution of a non-local boundary value problem with discontinuous matching condition for the loaded equation. Considering parabolic-hyperbolic type equations involves the Caputo fractional derivative and loaded part joins in Riemann-Liouville integrals. The uniqueness of a solution is proved by the method of integral...
We study a boundary value problem for a system of two pseudoparabolic equations when for one of the functions the initial data and its values at the final time are given. Existence and uniqueness theorems for this problem are proven with the help of the properties of solutions to some nonlocal and inverse problems for a pseudoparabolic equation which are established in this article.
We study a one-dimensional system of two parabolic loaded equations of a special kind and a one-dimensional composite-type system of a special kind. Both systems are considered with Cauchy data. We obtain sufficient conditions for the existence of a solution in the class of bounded smooth functions. The method of splitting on the differential level (the weak approximation method) is used in the proof.
In this paper the unique solvability of the analog of the Tricomi problem for the third order loaded differential and integro-differential equations with parabolic-hyperbolic operators is proved. The existence of a solution is proved by the reduction to the integral equations with a shift of the second kind. We obtain necessary and sufficient conditions for the existence of a unique solution.
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