Anshul Sharma, Suyash Narayan Mishra, Anurag Shukla
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.
DOI: 10.58997/ejde.conf.27.s1
Show me the PDF file (372 K), TEX file for this article.
 |
Anshul Sharma Department of Applied Sciences and Humanities Institute of Engineering and Technology Lucknow-226027, Uttar Pradesh, India email: anshkaushik9897@gmail.com |
|---|---|
 |
Suyash Narayan Mishra Department of Applied Sciences and Humanities Institute of Engineering and Technology Lucknow-226027, Uttar Pradesh, India email: snmishra@ietlucknow.ac.in |
 |
Anurag Shukla Department of Applied Sciences and Humanities Rajkiya Engineering College Kannauj-209732, Uttar Pradesh, India email: anuragshukla259@gmail.com |
Return to the table of contents
for this conference.
Return to the EJDE web page