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...

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Bibliographic Details

Main Authors:	Alsa’Di, Kawthar, Nik Long, Nik Mohd Asri
Format:	Article
Language:	en
Published:	International Scientific Research Publications 2025
Subjects:	Computational Mechanics Mathematics (all)
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
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