SPECTRAL OPTIMAL CONTROL SOLUTION FOR NONLINEAR WEAKLY SINGULAR SYSTEM OF FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

Hussien Shafei Hussien () and Mohamed Abdalla
Additional contact information
Hussien Shafei Hussien: Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
Mohamed Abdalla: Mathematics Department, Faculty of Science, King Khalid University, Abha, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-11

Abstract: This research introduces an innovative numerical method for addressing a specific category of nonlinear weakly singular fractional integro-differential equations (NWSFIDEs). The proposed approach primarily involves utilizing the Riemann–Liouville fractional-order integral definition to avoid the issue of singularity in the core problem. Then, Genocchi operational integration matrix of fractional order is presented to fully approximate the fractional-order integral. To determine the fractional-order derivative of the unknown function, we employed a series of partially wavelet-based fractional-order Mittag-Leffler functions (PWBFMLFs). To develop the proposed numerical method, the core problem is reformulated as an equivalent optimal control problem involving a specific experimental function. Theorems for error and convergence analysis of the proposed techniques are examined. Theoretical predictions are validated through numerical examples, which show that the proposed method, requiring fewer degrees of freedom, surpasses existing methods.

Keywords: Generalized Fractional Mittag-Leffler Function; Partly Wavelet Function; Genocchi Polynomials; Operational Matrix; Optimal Control Problem (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X25401449
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:33:y:2025:i:08:n:s0218348x25401449

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X25401449

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().