UNAMBIGUOUS SOLVABILITY OF A PARTICULAR CASE OF SYSTEMS OF INTEGRO-DIFFERENTIAL EQUATIONS WITH A PULSED KAEV DISTANCE CONTAINING A PARAMETER

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Abstract

As is known, one of the special cases of integro – differential equations is the so-called fractional differential equations. In this paper, we consider a boundary value problem for systems of integro-differential equations with a conformable derivative. The parameterization method proposed by Professor D. Dzhumabaev was applied to this problem. New parameters are introduced, and based on these parameters, we move to new variables. The transition to new variables makes it possible to obtain the initial conditions for the equation. Based on this, the solution of the problem is reduced to the solution of a special Cauchy problem and a system of linear equations. Using the fundamental matrix of the main part of the differential equation, an integral equation of the Volterra type is obtained. The method of sequential approximation determines the unique solution of the integral equation. Based on this, they find a solution to the special Cauchy problem and put it in boundary conditions. On the basis of the obtained system of linear equations, the necessary and sufficient conditions for an unambiguous solution of the initial problem are established.