On solvability of a multipoint boundary value problem for integro-differential equations with a conformable derivative Available to Purchase

It is known that one of the special cases of integro-differential equations is the so-called differential equations of fractional order. In this paper, we consider a multipoint boundary value problem for an involutively transformed integro-differential equation with a conformable derivative. Using the property of the involutive transformation, the problem is reduced to a multi-point boundary value problem for integro-differential equations. Further, the parameterization method proposed by Professor D. Dzhumabaev is applied to the problem. New parameters are introduced, and based on these parameters, we transfer them to new variables. The transition to new variables makes it possible to obtain initial conditions for the equation. The method of successive approximation determines the unique solution of the integral equation. Substituting the obtained solution into the boundary conditions, we obtain a system of linear equations with respect to the introduced parameters. A connection is established between the reversibility of the matrix of the resulting system and the unique solvability of the original problem.