INVESTIGATION OF SOLUTIONS OF PARTIAL INTEGRO-DIFFERENTIAL EQUATION OF FOURTH ORDER BY MEANS OF A NEW WAY

Ashirbayeva Aizharkyn Zhorobekovna; Zholdoshova Chebire Burkanovna

doi:10.5281/zenodo.10113338

Ashirbayeva Aizharkyn Zhorobekovna, Zholdoshova Chebire Burkanovna

Abstract. This article discusses the partial integro-differential equation of fourth order. To solve the problem, a new method is used, with the help of which we will bring the partial integro-differential equation of fourth order to a form convenient for using the additional argument method. The initial problem for a fourth-order equation is first reduced to a system of second-order partial differential equations. And the system of equations in partial derivatives of the second order is reduced by the method of an additional argument to a system of integral equations, for which the principle of compressive reflections is applied.

Keywords: integro-differential, partial derivatives, additional argument method, initial problem, integral equation, contraction mapping principle, fourth order

References:

1. Ashirbaeva A.J., Zholdoshova Ch.B. Solving of non-linear partial integro-differential equation of hyperbolictype (in Russian). Bulletin of OshSU, series of natural and medical sciences, 2012, No. 2, issue 1, pp. 144-149. 2. Ashirbaeva A.J., Zholdoshova Ch.B. Invertigation of solutions of partial integro-differential equation (in Russian). Bulletin of OshSU, series of natural and medical sciences, 2012, No. 2, issue 1, pp. 150-153. 3. Ashirbaeva A.J., Mamaziyaeva E.A. New way to build solutions of partial differential equations of the fourth order of hyperbolic type (in Russian). Eurasian Scientific association, 2019, No. 2-1(48), pp. 6-9.