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 | ||
| 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 | ||
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