On the existence of a positive solution to a boundary value problem for a nonlinear functional-differential equation of fractional order

Authors

UDC

517.927.4

DOI:

https://doi.org/10.31429/vestnik-20-3-6-12

Abstract

The following boundary value problem for a non-linear functional-differential equation of fractional order is considered:
\begin{align*}
&D_{0+}^\alpha x(t)+f \left (t,\left(Tx \right)(t) \right)=0,\quad 0<t<1, \quad \alpha\in (2, 3],\\
&x(0)=x'(0)=0,\\
&x(1)=0.
\end{align*}
Using special topological tools of nonlinear analysis, we prove the existence of a positive solution to this problem. An example is given that illustrates the fulfillment of sufficient conditions for the unique solvability of the problem. The results obtained complement the author's research on the existence and uniqueness of positive solutions to boundary value problems for non-linear functional-differential equations.

Keywords:

functional-differential equation of fractional order, положительное решение, краевая задача, функция Грина

Acknowledgement

The study did not have sponsorship.

Author Info

Gusen E. Abduragimov

канд. физ.-мат. наук, доцент кафедры прикладной математики Дагестанского государственного университета

e-mail: gusen_e@mail.ru

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Issue

2023. Vol. 20. No. 3

Section

Mathematics

Pages

6-12

Submitted

2023-06-23

Published

2023-09-29

How to Cite

Abduragimov G.E. On the existence of a positive solution to a boundary value problem for a nonlinear functional-differential equation of fractional order. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2023, vol. 20, no. 3, pp. 6-12. DOI: https://doi.org/10.31429/vestnik-20-3-6-12 (In Russian)

Copyright (c) 2023 Abduragimov G.E.

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