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Study of the problem of one-dimensional flow of homogenous fluids in fractal porous media
(Springer Science and Business Media Deutschland GmbH, 2024) Aliyev, Nihan; Rasulov, Mahir; Sinsoysal, Bahaddin
In this paper, for the first time the exact solution in the form of Mittag-Leffler series for the initial-boundary problem of the fractional differential equation is obtained expressing the process of one-dimensional motion in porous medium with complex permeability homogeneous fluid to gallery. The obtained result permits the theoretical calculations in the process of exploitation of oil fields with a fractal nature.
The boundary value problem for an ordinary linear half-order differential equation
(E.A. Buketov Karaganda University Publish House, 2024) Aliyev, Nihan; Rasulov, Mahir; Sinsoysal, Bahaddin
This study is devoted to the study of the solution of a boundary value problem for an ordinary linear differential equation of half order with constant coefficients. Using of the fundamental solution of the main part of the considered equation, we obtained the principal relations, from which we obtain the necessary conditions for the Fredholm property of the original problem. Further, using the Mittag-Leffler function, a general solution of the homogeneous equation is obtained. Finally, the problem under consideration is reduced to an integral Fredholm equation of the second kind with a non-singular kernel, i.e., the Fredholm property of the stated problem is proved.