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Numerical Simulation of Fractional Delay Differential Equations Using the Operational Matrix of Fractional Integration for Fractional-Order Taylor Basis
| Content Provider | MDPI |
|---|---|
| Author | Ibrahim, Avcı |
| Copyright Year | 2021 |
| Description | In this paper, we consider numerical solutions for a general form of fractional delay differential equations (FDDEs) with fractional derivatives defined in the Caputo sense. A fractional integration operational matrix, created using a fractional Taylor basis, is applied to solve these FDDEs. The main characteristic of this approach is, by utilizing the operational matrix of fractional integration, to reduce the given differential equation to a set of algebraic equations with unknown coefficients. This equation system can be solved efficiently using a computer algorithm. A bound on the error for the best approximation and fractional integration are also given. Several examples are given to illustrate the validity and applicability of the technique. The efficiency of the presented method is revealed by comparing results with some existing solutions, the findings of some other approaches from the literature and by plotting absolute error figures. |
| Starting Page | 10 |
| e-ISSN | 25043110 |
| DOI | 10.3390/fractalfract6010010 |
| Journal | Fractal and Fractional |
| Issue Number | 1 |
| Volume Number | 6 |
| Language | English |
| Publisher | MDPI |
| Publisher Date | 2021-12-26 |
| Access Restriction | Open |
| Subject Keyword | Fractal and Fractional Industrial Engineering Fractional Delay Differential Equations Numerical Solutions Fractional Taylor Basis Operational Matrix Riemann–liouville Fractional Integral Caputo Fractional Derivative |
| Content Type | Text |
| Resource Type | Article |
