Nonlinear higher order fractional terminal value problems

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 7; no. 5; pp. 7489 - 7506
Main Authors Baleanu, Dumitru, Shiri, Babak
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
existence
piecewise polynomials collocation methods
regularity
systems of fractional differential equations
terminal value problems
weakly singular volterra and fredholm integral equations
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022420

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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2022420