Results on generalized neutral fractional impulsive dynamic equation over time scales using nonlocal initial condition

Abstract

This paper explored the existence and uniqueness of a neutral fractional impulsive dynamic equation over time scales that included nonlocal initial conditions and employed the Caputo-nabla derivative (C$ \nabla $D). The establishment of existence and uniqueness relies on the fine fixed point theorem. Furthermore, a comparison was conducted between the fractional order C$ \nabla $D and the Riemann-Liouville nabla derivative (RL$ \nabla $D) over time scales. Theoretical findings were substantiated through a numerical methodology, and an illustrative graph using MATLAB was presented for the provided example.

Keywords

• neutral differential equations
• c$ \nabla $d
• rl$ \nabla $d
• time scales