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\begin{document}

\title{Reproducing kernel approach for numerical solutions of fuzzy fractional
initial value problems under the Mittag-Leffler kernel differential
operator}



\author[1]{omar abu arqub}%
\author[2]{Jagdev Singh}%
\author[3]{Banan  Maayah }%
\author[4]{Mohammed Alhodaly}%
\affil[1]{Al-Balqa' Applied University}%
\affil[2]{JECRC University}%
\affil[3]{The University of Jordan}%
\affil[4]{King Abdulaziz University}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{abstract}
In this research study, fuzzy fractional differential equations in
presence of the Atangana-Baleanu-Caputo differential operators are
analytically and numerically treated using extended reproducing Kernel
Hilbert space technique. With the utilization of a fuzzy strongly
generalized differentiability form, a new fuzzy characterization theorem
beside two fuzzy fractional solutions is constructed and computed. To
besetment the attitude of fuzzy fractional numerical solutions; analysis
of convergence and conduct of error beyond the reproducing kernel theory
are explored and debated. In this tendency, three computational
algorithms and modern trends in terms of analytic and numerical
solutions are propagated. Meanwhile, the dynamical characteristics and
mechanical features of these fuzzy fractional solutions are demonstrated
and studied during two applications via three-dimensional graphs and
tabulated numerical values. In the end, highlights and future suggested
research work are eluded.%
\end{abstract}%



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