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Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix

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Abstract

This paper presents the generalized nonlinear delay differential equations of fractional variable-order. In this article, a novel shifted Jacobi operational matrix technique is introduced for solving a class of multi-terms variable-order fractional delay differential equations via reducing the main problem to an algebraic system of equations that can be solved numerically. The suggested technique is successfully developed for the aforementioned problem. Comprehensive numerical experiments are presented to demonstrate the efficiency, generality, accuracy of proposed scheme and the flexibility of this method. The numerical results compared it with other existing methods such as fractional Adams method (FAM), new predictor–corrector method (NPCM), a new approach, Adams–Bashforth–Moulton algorithm and L1 predictor–corrector method (L1-PCM). Comparing the results of these methods as well as comparing the current method (NSJOM) with the exact solution, indicating the efficiency and validity of this method. Note that the procedure is easy to implement and this technique will be considered as a generalization of many numerical schemes. Furthermore, the error and its bound are estimated.

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Acknowledgements

We are grateful to two anonymous reviewers for their helpful comments, which undoubtedly led to the definite improvements in the paper.

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  1. Department of Applied Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34149, Iran

    H. R. Khodabandehlo, E. Shivanian & S. Abbasbandy

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  1. H. R. Khodabandehlo
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  2. E. Shivanian
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  3. S. Abbasbandy
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Correspondence to E. Shivanian.

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Khodabandehlo, H.R., Shivanian, E. & Abbasbandy, S. Numerical solution of nonlinear delay differential equations of fractional variable-order using a novel shifted Jacobi operational matrix. Engineering with Computers 38 (Suppl 3), 2593–2607 (2022). https://doi.org/10.1007/s00366-021-01422-7

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