Solvability Of The Functional Integro-Differential Equations Of Fractional-Order And Neural Network Approximation | ||||
| Al-Azhar Bulletin of Science | ||||
| Articles in Press, Accepted Manuscript, Available Online from 03 August 2025 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/absb.2025.445623 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Mohamed M. El-Hawary  ; Abd El-Wahab Abbas Ragab; Hassan A. Elshenbary ; Reda Gamal Ahmed ; Ahmed A. El-Deeb
| ||||
| Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City, Cairo, Egypt. | ||||
| Abstract | ||||
| In this paper, we apply Schauder’s fixed point theorem to establish the existence of solutions to a fractional-order nonlinear integro-differential equations with nonlocal condition. We demonstrate the unique solution and its continuous dependence on the initial data E0 and the functional φ . An example is provided to illustrate our results. Additionally, the Picard method and neural networks are employed to approximate the solution. | ||||
| Keywords | ||||
| Functional integro–differential equations; Fractional-order; Liouville-Caputo fractional derivative; Existence of solutions; Schauer’s fixed point theorem; Unique solution; Continuous dependence | ||||
|
Statistics Article View: 52 |
||||
