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Numerical solution of fractional differential equations using hybrid Bernoulli polynomials and block pulse functions

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Abstract

Block pulse functions are piecewise constant and not smooth enough. Therefore, they offer limited accuracy when used to approximate functions and unable to find highly accurate numerical solutions of fractional differential equations (FDEs). To overcome this problem, we present in this paper a new efficient numerical method for solving FDEs. A hybrid Bernoulli polynomials and block pulse functions operational matrix of fractional order integrals is derived and used to convert the underlying FDEs into a system of algebraic equations. The solutions of the FDEs are obtained by solving the algebraic equations. Simulation examples are given to verify the effectiveness of our proposed method, and the results show that the method is much more efficient and accurate than other known methods.

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Acknowledgements

This work is partially supported by the National Natural Science Foundation of China (No. 61771418).

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Authors and Affiliations

  1. Institute of Electrical Engineering, Yanshan University, Qinhuangdao, 066004, Hebei, China

    Bo Zhang & Yinggan Tang

  2. LiRen College of Yanshan University, Qinghuangdao, 066004, Hebei, China

    Bo Zhang

  3. School of Communication Engineering, HangZhou Dianzi University, Hang Zhou, 310018, Zhejiang, China

    Xuguang Zhang

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  1. Bo Zhang
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  2. Yinggan Tang
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Correspondence to Yinggan Tang.

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Zhang, B., Tang, Y. & Zhang, X. Numerical solution of fractional differential equations using hybrid Bernoulli polynomials and block pulse functions. Math Sci 15, 293–304 (2021). https://doi.org/10.1007/s40096-021-00379-4

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  • DOI: https://doi.org/10.1007/s40096-021-00379-4

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