A hybrid technique of deep learning neural networks with finite difference method for higher order fractional Volterra-Fredholm integro-differential equations with φ-Caputo operator
This paper deals with the theoretical and numerical aspects for higher order Volterra-Fredholm fractional integro-differential equations (VF-IDEs) under φ-Caputo operator. Using Liptchiz conditions, Krasnoselskii’s fixed point theorem, and Gronwall inequality with respect to the function φ, existenc...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | en |
| Published: |
International Scientific Research Publications
2025
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/122360/1/122360.pdf http://psasir.upm.edu.my/id/eprint/122360/ https://www.isr-publications.com/jmcs/articles-15434-a-hybrid-technique-of-deep-learning-neural-networks-with-finite-difference-method-for-higher-order-fractional-olterra-fredholm-integro-differential-equations-with-varphi-caputo-operator |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Internet
http://psasir.upm.edu.my/id/eprint/122360/1/122360.pdfhttp://psasir.upm.edu.my/id/eprint/122360/
https://www.isr-publications.com/jmcs/articles-15434-a-hybrid-technique-of-deep-learning-neural-networks-with-finite-difference-method-for-higher-order-fractional-olterra-fredholm-integro-differential-equations-with-varphi-caputo-operator