Generalized Fractional Operators on Time Scales with Application to Dynamic Equations

TL;DR

This paper develops generalized fractional calculus operators on time scales and establishes conditions for the existence and uniqueness of solutions to related differential equations, bridging continuous and discrete analysis.

Contribution

It introduces broader definitions of fractional integrals and derivatives on time scales and proves solution existence and uniqueness for associated initial value problems.

Findings

Generalized fractional operators on time scales are defined.

Sufficient conditions for solution existence are established.

Uniqueness of solutions to fractional dynamic equations is proved.

Abstract

We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value problem described by generalized fractional order differential equations on time scales are proved.