Open AccessNonlinear higher order fractional terminal value problems
Author(s) -
Dumitru Băleanu,
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Babak Shiri,
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Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022420
Subject(s) - mathematics , discretization , piecewise , nonlinear system , convergence (economics) , terminal (telecommunication) , polynomial , initial value problem , fixed point theorem , order (exchange) , collocation (remote sensing) , mathematical analysis , fractional calculus , computer science , physics , telecommunications , finance , quantum mechanics , machine learning , economics , economic growth
Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.