Mild and classical solutions to fractional Cauchy problem on time scales

Abstract

In this manuscript, aims to examine the uniqueness and existence of impulsive non-local conditions, as well as classical and mild solutions to the fractional Cauchy problem in time scales. The main results are derived by the Gronwall inequality and the Banach fixed point theorem in time scales. Eventually, we offered an example to demonstrate the suitability of the conclusions on the fractional Cauchy issue on a time scale.

Keywords

• Time scale
• Fractional calculus
• Fractional differential equations
• Cauchy problem
• Nonlocal conditions
• Impulsive equations