\(\psi\)-CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH MAXIMA ON TIME SCALES

In this paper, we demonstrate the existence and uniqueness of solutions for a class of initial value problems in differential equations with maxima, involving the \(\psi\) $\psi$ -Caputo fractional order on time scales. Our main theorem is established through the application of the contraction principle of Banach, employing a combination of Picard and weak Picard operator techniques to obtain data dependence results on the parameters. Furthermore, an illustrative example is provided to demonstrate the practical utility of our theoretical findings.