A PREDICTOR-CORRECTOR METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

SALIHI, Ylldrita and XHAFERI, Miranda and RASIMI, Krutan and M. JONUZI, Verda (2022) A PREDICTOR-CORRECTOR METHOD FOR SOLVING DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER. Journal of Natural Sciences and Mathematics of UT, 7 (13-14). pp. 158-165. ISSN 2671-3039

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Abstract

The story of the fractional calculus began with that letter in 1695, answered by Leibniz. Classical analysis is not always sufficient, for real problems, constructed by using mathematical expressions, for solving their applications in engineering, science, and many other fields. The aim of this paper is to show the effectiveness of the numerical predictor-corrector method known as Fractional Adams-Bashforth-Moulton method (FABM) by its application on solving different types of nonlinear differential equations of fractional order 0<α<1. It contains a short survey of basic numerical method (FABM) using the fractional derivative defined by Caputo. The equivalence between an ordinary differential equation of fractional order and a suitable Volterra integral equation is key to the approaches. The numerical results for the constructed method are compared with the exact solution for each equation by using absolute error (absolute difference between the exact and approximate solution at each integration point).The method is very simple and very much effective for solving differential equations of fractional order, it may be used. The behavior of the approximate time-series solutions are tabulated and plotted at different values of the fractional orders. During the work, it became necessary to use such symbolic software packages as Mathematica 12.1 in completing the required steps of the above procedures.

Item Type:	Article
Uncontrolled Keywords:	Fractional initial-value problem, Caputo fractional derivative, Volterra equation, Fractional Adams-Bashforth-Moulton method, Exact solution
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User:	Unnamed user with email zshi@unite.edu.mk
Date Deposited:	31 Oct 2022 13:38
Last Modified:	31 Oct 2022 13:38
URI:	http://eprints.unite.edu.mk/id/eprint/1073

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