Existence of Solutions for $\phi$-Caputo Fractional Hybrid Boundary Value Problem on Time Scales

Abstract

This study explores the existence of solutions for a class of fractional hybrid differential equations incorporating maxima and \(\phi\)-Caputo derivatives on time scales. The proofs are derived using Dhage's fixed point theorem and essential techniques from \(\phi\)-fractional calculus on time scales.  To demonstrate the applicability and effectiveness of the results, an illustrative example is presented.