 An efficient numerical method based on Fibonacci polynomials to solve fractional differential equationsOctavian Postavaru Mathematics and Computers in Simulation (MATCOM), 2023, vol. 212, issue C, 406-422 Abstract: The Fibonacci sequence is significant because of the so-called golden ratio, which describes predictable patterns for everything. Fibonacci polynomials are related to Fibonacci numbers, and in this paper we extend their applicability by using them to solve fractional differential equations (FDEs) and systems of fractional differential equations (SFDEs). With the help of the Riemann–Liouville fractional integral operator for the fractional-order hybrid function of block-pulse functions and the Fibonacci polynomials defined in this paper, the solution of the considered FDE and SFDE is reduced to a system of algebraic equations, which can be solved by Newton’s iterative method. The fractional order is obtained by transforming x into xα, with α>0. Compared to other models, our method in some situations is better by twelve orders of magnitude. There are situations when we get the exact solution. The presented method proves to be simple and effective in solving nonlinear problems with given initial values. Keywords: Fractional-order; Hybrid functions; Block-pulse; Fibonacci polynomials; Hypergeometric function (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:212:y:2023:i:c:p:406-422 DOI: 10.1016/j.matcom.2023.04.028 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.