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

Author:

Morsy Ahmed1,Anusha C.2,Nisar Kottakkaran Sooppy34,Ravichandran C.2

Affiliation:

1. Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia

2. Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029, India

3. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

4. Saveetha School of Engineering, SIMATS, Chennai, India

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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