On the existence of a positive solution to a boundary value problem for a nonlinear functional-differential equation of fractional order
UDC
517.927.4EDN
CYWMKYDOI:
10.31429/vestnik-20-3-6-12Abstract
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 ГринаFunding information
The study did not have sponsorship.
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Dates
Submitted
June 23, 2023
Accepted
July 10, 2023
Published
September 29, 2023
How to Cite
[1]
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, т. 20, № 3, pp. 6–12. DOI: 10.31429/vestnik-20-3-6-12
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