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\begin{document}

\title{Existence and stability of positive solutions for a Hadamard-type
fractional two-point boundary value problem}



\author[1]{Huijuan Zhu}%
\author[2]{Fanglei Wang}%
\affil[1]{Hohai University}%
\affil[2]{College of Science, Hohai University}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\begin{abstract}
In this paper,we mainly establish existence and uniqueness of positive
solution for the Hadamard-type fractional two-point boundary value
problem
(\textbackslash{}mathcal\{D\}\^{}\{\selectlanguage{greek}α\selectlanguage{english}\}\_\{1\^{}\{+\}\}x(t))'`+\selectlanguage{greek}λ\selectlanguage{english}\^{}2
\textbackslash{}mathcal\{D\}\^{}\{\selectlanguage{greek}α\selectlanguage{english}\}\_\{1\^{}\{+\}\}x(t)+f(t,x(t),-\textbackslash{}mathcal\{D\}\^{}\{\selectlanguage{greek}α\selectlanguage{english}\}\_\{1\^{}\{+\}\}x(t))=0,
t[?] (1,e), x(1)=x'(1)=x'(e)=0 ,
\textbackslash{}mathcal\{D\}\^{}\{\selectlanguage{greek}α\selectlanguage{english}+1\}\_\{1\^{}\{+\}\}x(1)=\textbackslash{}mathcal\{D\}\^{}\{\selectlanguage{greek}α\selectlanguage{english}+1\}\_\{1\^{}\{+\}\}x(e)=0,
by using the fixed point theorems. In addition, we also study the
Ulam-Hyers-Rassias stability of the related problem. On the other hand,
when f(t,u,v) is singular at u=0 and v=0, we study the existence and
uniqueness of its solution. Finally, some examples are included to show
the applicability of our results.%
\end{abstract}%



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\textbf{Hosted file}

\verb`z.4.tex`  available at \url{https://authorea.com/users/481532/articles/568535-existence-and-stability-of-positive-solutions-for-a-hadamard-type-fractional-two-point-boundary-value-problem}

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