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Abstract
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Previous studies have shown that fractional derivative operators have become an integral
part of modeling natural and physical phenomena. During the progress and evolution of these
operators, it has become clear to researchers that each of these operators has special capacities for
investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point
theory and its famous contractions have always served as useful tools in these studies. In this regard,
in this work, we considered the Hilfer-type fractional operator to study the proposed
integrodifferential equation. We have used the capabilities of measure theory and fixed point
techniques to provide the required space to guarantee the existence of the solution. The Schauder and
Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, we provided
two examples with some graphical and numerical simulation to make our results more objective.
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