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Abstract
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In this work, we analyze a q-fractional jerk problem having anti-periodic boundary conditions. The focus is on investigating that whether a unique solution exists and remains stable under specific conditions. To prove the uniqueness of the solution, we employ a Banach fixed point theorem and a mathematical tool for establishing the presence of distinct fixed points. To demonstrate the availability of a solution, we utilize Leray Schauder's alternative, a method commonly employed in mathematical analysis. Furthermore, we examine and introduce different kinds of stability concepts, for the given problem. In conclusion, we present several examples to illustrate and validate the outcomes of our study.
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