Fractional conformable differential time-delayed problems: Theoretical analysis and numerical implementation using reproducing Hilbert’s approximate scheme

Roumaissa Benseghir, Omar Abu Arqub and Banan Maayah
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Roumaissa Benseghir: Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan
Omar Abu Arqub: ��Department of Mathematics, Faculty of Science, Al-Balqa’ Applied University, Salt 19117, Jordan
Banan Maayah: Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, Jordan

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 02, 1-23

Abstract: The intention of this analysis is to declare and demonstrate the complete foundational theorem of existence and uniqueness for fractional conformable initial value time-delayed models incorporating time delays. The utilized proof is based on Picard’s iterative method and the fixed point theorem. Thereafter, to showcase the outcomes of our theoretical research and as an application for numerical solutions, we propose an effective numerical method based on the reproducing kernel Hilbert approximation to solve some fractional time-delayed problems. Afterward, the construction of appropriate Hilbert spaces, derivation of the kernel functions, representation of the unique delayed solution and algorithm solution steps are also discussed and utilized. Indeed, the series solution, the convergence, and the error analysis outcomes are debated and discussed. For comparative analysis, we describe our gained results in the constructed tables and figures which help us to compare the numerical solution with the exact one. Concluding notes, keynotes and future are listed in the closing portion.

Keywords: Time-delayed fractional differential problem; existence and uniqueness foundational theorem; reproducing kernel algorithm; fractional conformable derivative; Picard’s iterative method; fixed point theorem; error analysis and convergence (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500219

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