An Efficient Numerical Approach for Solving Systems of Fractional Problems and Their Applications in Science

Sondos M. Syam, Z. Siri, Sami H. Altoum and R. Md. Kasmani ()
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Sondos M. Syam: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Z. Siri: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Sami H. Altoum: Department of Mathematics, AL-Qunfudhah University College, Umm Al-Qura University, Al Qunfudhah 24382, Saudi Arabia
R. Md. Kasmani: Institute of Mathematical Sciences, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2023, vol. 11, issue 14, 1-21

Abstract: In this article, we present a new numerical approach for solving a class of systems of fractional initial value problems based on the operational matrix method. We derive the method and provide a convergence analysis. To reduce computational cost, we transform the algebraic problem produced by this approach into a set of 2 × 2 nonlinear equations, instead of solving a system of 2 m × 2 m equations. We apply our approach to three main applications in science: optimal control problems, Riccati equations, and clock reactions. We compare our results with those of other researchers, considering computational time, cost, and absolute errors. Additionally, we validate our numerical method by comparing our results with the integer model when the fractional order approaches one. We present numerous figures and tables to illustrate our findings. The results demonstrate the effectiveness of the proposed approach.

Keywords: optimal control problems; Riccati equations; operational matrix method; vitamin C clock reaction; fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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