Nonlinear system of fractional dynamic equations involving initial and boundary conditions

Nonlinear system of fractional dynamic equations

Abstract

This paper presents a comprehensive investigation into the existence and uniqueness of solutions
for nonlinear fractional dynamic equations defined on time scales. Both initial and boundary value problems
are considered, and the solvability of the equations is examined through the application of fixed point theory.
The theoretical framework is developed using fundamental concepts, lemmas, and propositions associated with
Riemann–Liouville and Caputo-type fractional derivatives. To illustrate the validity and applicability of the
established results, two representative examples are provided.