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

Snezhana Hristova, Kremena Stefanova and Angel Golev
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Snezhana Hristova: Department of Applied Mathematics and Modeling, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria
Kremena Stefanova: Department of Computer Technologies, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria
Angel Golev: Department of Software Technologies, University of Plovdiv “Paisii Hilendarski”, Plovdiv 4000, Bulgaria

Mathematics, 2020, vol. 8, issue 4, 1-16

Abstract: 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.

Keywords: Riemann-Liouville fractional differential equation; delay; lower and upper solutions; monotone-iterative technique (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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