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\begin{document}

\title{Solutions of sum-type singular fractional q-integro-differential
equation with \$m\$-point boundary value using quantum calculus}



\author[1]{Ali Ahmadian}%
\author[2]{Shahram Rezapour}%
\author[3]{Soheil Salahshour}%
\author[4]{Mohammad Esmael Samei}%
\affil[1]{Mediterranean University of Reggio Calabria Department of Informatics Mathematics Electronics and Transport}%
\affil[2]{Azarbaijan Shahid Madani University}%
\affil[3]{Bahcesehir Universitesi}%
\affil[4]{Bu Ali Sina University}%


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  \date{June 14, 2024}


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\begin{abstract}
In this study, we investigate the sum-type singular nonlinear fractional
q-integro-differential \$m\$-point boundary value problem. The existence
of positive solutions is obtained by the properties of the Green
function, standard Caputo \$q\$-derivative, Riemann-Liouville fractional
\$q\$-integral and the means of a fixed point theorem on a real Banach
space \$(\textbackslash{}mathcal\{X\},
\textbackslash{}\textbar{}.\textbackslash{}\textbar{})\$ which has a
partially order by using a cone \$P \textbackslash{}subset
\textbackslash{}mathcal\{X\}\$. The proofs are based on solving the
operator equation \$\textbackslash{}mathcal\{O\}\_1 x +
\textbackslash{}mathcal\{O\}\_2 x = x \$ such that the operator
\$\textbackslash{}mathcal\{O\}\_1\$, \$\textbackslash{}mathcal\{O\}\_2\$
are \$r\$-convex, sub-homogeneous, respectively and define on cone
\$P\$. As applications, we provide an example illustrating the primary
effects.%
\end{abstract}%



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