MULTIQUADRIC QUASI-INTERPOLATION METHOD FOR FRACTIONAL INTEGRAL-DIFFERENTIAL EQUATIONS

Ziqiang Wang; Qing Tan; Zhongqing Wang; Junying Cao

doi:10.11948/20230011

2024 Volume 14 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2024 > 14(5): 2534-2557

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Ziqiang Wang, Qing Tan, Zhongqing Wang, Junying Cao. MULTIQUADRIC QUASI-INTERPOLATION METHOD FOR FRACTIONAL INTEGRAL-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2534-2557. doi: 10.11948/20230011

Citation:

Ziqiang Wang, Qing Tan, Zhongqing Wang, Junying Cao. MULTIQUADRIC QUASI-INTERPOLATION METHOD FOR FRACTIONAL INTEGRAL-DIFFERENTIAL EQUATIONS[J]. Journal of Applied Analysis & Computation, 2024, 14(5): 2534-2557. doi: 10.11948/20230011

MULTIQUADRIC QUASI-INTERPOLATION METHOD FOR FRACTIONAL INTEGRAL-DIFFERENTIAL EQUATIONS

1.
School of Data Science and Information Engineering, Guizhou Minzu University, 550025 Guiyang, China
2.
Basic Teaching Department, Shandong Huayu University of Technology, 253034 Dezhou, China

Author Bio: Email: wangzq@lsec.cc.ac.cn(Z. Wang); Email: 2218244682@qq.com(Q. Tan); Email: wangzhongqing1999@126.com(Z. Wang)
Corresponding author: Email: caojunying@gzmu.edu.cn(J. Cao)
Fund Project: Z. Wang (Ziqiang Wang) was supported by National Natural Science Foundation of China (Grant No. 11961009) and Foundation of Guizhou Science and Technology Department (Grant No. QHKJC-ZK[2024]YB497).J. Cao was supported by National Natural Science Foundation of China (Grant Nos. 12361083, 62341115) and Science research fund support project of the Guizhou Minzu University (Grant No. GZMUZK[2023]CXTD05).Z. Wang (Ziqiang Wang) and J. Cao were supported by Natural Science Research Project of the Department of Education of Guizhou Province (Grant Nos. QJJ2023012, QJJ2023062, QJJ2023061)

Abstract

Abstract

In this paper, Multiquadric quasi-interpolation method is used to approximate fractional integral equations and fractional differential equations. Firstly, we construct two operators for approximating the Hadamard integral-differential equation based on quasi interpolators, and verify their properties and order of convergence. Secondly, we obtain that the approximation order of the numerical integral scheme is 3, and the approximation order of the numerical scheme is 3-μ for μ(0 < μ < 1) order fractional Hadamard derivative. Finally, the results of numerical experiments show that the numerical results are in agreement with the theoretical analysis.
- Multiquadric quasi-interpolation /
- fractional integral-differential equations /
- Hadamard derivative and integral /
- error analysis
MSC: 65R20, 65D30

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References

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