Third International Conference on Applications of Mathematics to Nonlinear Sciences.
Electron. J. Diff. Eqns., conf. 27 (2024), pp. 49-62.

Title: Asymptotic stability for Hilfer-like nabla nonlinear fractional difference equations

Authors: Anshul Sharma (Institute of Engineering and Tech., Uttar Pradesh, India)
             Suyash Narayan Mishra (Institute of Engineering and Tech., Uttar Pradesh, India)
              Anurag Shukla (Rajkiya Engineering College,  Uttar Pradesh, India)
 
Abstract: 
This article examines the asymptotic stability of nonlinear fractional 
difference equations  with a Hilfer-like nabla operator. 
The results for a Hilfer-type nabla fractional 
difference that contains Riemann-Liouville and 
Caputo nabla difference as a particular case. 
We use Picard's iteration  and a fixed point theorem to 
obtain results on existence and uniqueness. 
To obtain the main results, we use linear a scalar fractional difference 
equality, discrete comparison principle, and basics of difference equations. 
We also present a Lyapunov second direct method for nonlinear discrete 
fractional systems. We also discus stability results with some numerical 
examples.

Published August 20, 2024.
Math Subject Classifications: 34D20, 26A33, 39A30.
Key Words: Hilfer-like nabla operator; asymptotic stability;  fractional difference equations; Lyapunov direct method.