ON EFFICIENT FRACTIONAL CAPUTO-TYPE SIMULTANEOUS SCHEME FOR FINDING ALL ROOTS OF POLYNOMIAL EQUATIONS WITH BIOMEDICAL ENGINEERING APPLICATIONS

Mudassir Shams, Nasreen Kausar, Cuauhtã‰moc Samaniego, Praveen Agarwal, Shams Forruque Ahmed and Shaher Momani
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Mudassir Shams: Department of Mathematics and Statistics, Riphah International University, Islamabad 44000, Pakistan
Nasreen Kausar: ��Department of Mathematics, Yildiz Technical University, Faculty of Arts and Science, Esenler, 34220 Istanbul, Turkey
Cuauhtã‰moc Samaniego: ��American University of the Middle East, Department of Mathematics and Statistics, Egaila 54200, Kuwait
Praveen Agarwal: �Department of Mathematics, Anand International, College of Engineering Jaipur, Rajasthan, India¶Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, Russian Federation∥Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
Shams Forruque Ahmed: *Science and Math Program, Asian University for Women, Chattogram 4000, Bangladesh
Shaher Momani: ��†Department of Mathematics, The University of Jordan, Amman 11942, Jordan

FRACTALS (fractals), 2023, vol. 31, issue 04, 1-15

Abstract: This research paper introduces a novel fractional Caputo-type simultaneous method for finding all simple and multiple roots of polynomial equations. Without any additional polynomial and derivative evaluations using suitable correction, the order of convergence of the basic Aberth–Ehrlich simultaneous method has been increased from three to α + 3. In terms of accuracy, residual graph, computational efficiency and computation CPU time, the newly proposed families of simultaneous methods outperforms existing methods in numerical applications.

Keywords: Optimal Order; Simultaneous Methods; Caputo-Type Derivative; Error Graph; Computational Efficiency; Computer Algorithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400753

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