NDLI: Enhancing the Accuracy of Solving Riccati Fractional Differential Equations

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Enhancing the Accuracy of Solving Riccati Fractional Differential Equations

Content Provider	MDPI
Author	Toma, Antonela Dragoi, Flavius Postavaru, Octavian
Copyright Year	2022
Description	In this paper, we solve Riccati equations by using the fractional-order hybrid function of block-pulse functions and Bernoulli polynomials (FOHBPB), obtained by replacing x with $xα$ , with positive $α$ . Fractional derivatives are in the Caputo sense. With the help of incomplete beta functions, we are able to build exactly the Riemann–Liouville fractional integral operator associated with FOHBPB. This operator, together with the Newton–Cotes collocation method, allows the reduction of fractional differential equations to a system of algebraic equations, which can be solved by Newton’s iterative method. The simplicity of the method recommends it for applications in engineering and nature. The accuracy of this method is illustrated by five examples, and there are situations in which we obtain accuracy eleven orders of magnitude higher than if $α=1$ .
Starting Page	275
e-ISSN	25043110
DOI	10.3390/fractalfract6050275
Journal	Fractal and Fractional
Issue Number	5
Volume Number	6
Language	English
Publisher	MDPI
Publisher Date	2022-05-20
Access Restriction	Open
Subject Keyword	Fractal and Fractional Industrial Engineering Hybrid Functions Caputo Derivative Riemann–liouville Integral
Content Type	Text
Resource Type	Article

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