An efficient numerical approach for solving systems of fractional problems and their applications in science
Document Type
Article
Publication Date
7-1-2023
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 x 2 nonlinear equations, instead of solving a system of 2 m x 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
Divisions
MathematicalSciences
Funders
Umm Al-Qura University [Grant No: 23UQU4310382DSR002]
Publication Title
Mathematics
Volume
11
Issue
14
Publisher
MDPI
Publisher Location
MDPI AG, Grosspeteranlage 5, CH-4052 BASEL, SWITZERLAND