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Open AccessArticle

Computer Simulation and Iterative Algorithm for Approximate Solving of Initial Value Problem for Riemann-Liouville Fractional Delay Differential Equations

1
Department of Applied Mathematics and Modeling, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria
2
Department of Computer Technologies, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria
3
Department of Software Technologies, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 477; https://doi.org/10.3390/math8040477
Received: 19 February 2020 / Revised: 28 March 2020 / Accepted: 29 March 2020 / Published: 1 April 2020
The main aim of this paper is to suggest an algorithm for constructing two monotone sequences of mild lower and upper solutions which are convergent to the mild solution of the initial value problem for Riemann-Liouville fractional delay differential equation. The iterative scheme is based on a monotone iterative technique. The suggested scheme is computerized and applied to solve approximately the initial value problem for scalar nonlinear Riemann-Liouville fractional differential equations with a constant delay on a finite interval. The suggested and well-grounded algorithm is applied to a particular problem and the practical usefulness is illustrated. View Full-Text
Keywords: Riemann-Liouville fractional differential equation; delay; lower and upper solutions; monotone-iterative technique Riemann-Liouville fractional differential equation; delay; lower and upper solutions; monotone-iterative technique
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Hristova, S.; Stefanova, K.; Golev, A. Computer Simulation and Iterative Algorithm for Approximate Solving of Initial Value Problem for Riemann-Liouville Fractional Delay Differential Equations. Mathematics 2020, 8, 477.

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