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Volume 7
Issue 5
10.3390/fractalfract7050402
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Article

Fractional-Order Accumulative Generation with Discrete Convolution Transformation

by
Tao Chen
Department of Mathematics, Communication University of China, Beijing 100024, China
Fractal Fract. 2023, 7(5), 402; https://doi.org/10.3390/fractalfract7050402
Submission received: 2 April 2023 / Revised: 6 May 2023 / Accepted: 12 May 2023 / Published: 16 May 2023
(This article belongs to the Special Issue Fractional-Order Circuits, Systems, and Signal Processing)
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Abstract

A new fractional accumulation technique based on discrete sequence convolution transform was developed. The accumulation system, whose unit impulse response is the accumulation convolution sequence, was constructed; then, the order was extended to fractional orders. The fractional accumulative convolution grey forecasting model GMr*(1,1) was established on the sequence convolution. From the viewpoint of sequence convolution, we can better understand the mechanism of accumulative generation. Real cases were used to verify the validity and effectiveness of the fractional accumulative convolution method.
Keywords: fractional accumulation; discrete sequence convolution transform; unit impulse; grey forecasting fractional accumulation; discrete sequence convolution transform; unit impulse; grey forecasting

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MDPI and ACS Style

Chen, T. Fractional-Order Accumulative Generation with Discrete Convolution Transformation. Fractal Fract. 2023, 7, 402. https://doi.org/10.3390/fractalfract7050402

AMA Style

Chen T. Fractional-Order Accumulative Generation with Discrete Convolution Transformation. Fractal and Fractional. 2023; 7(5):402. https://doi.org/10.3390/fractalfract7050402

Chicago/Turabian Style

Chen, Tao. 2023. "Fractional-Order Accumulative Generation with Discrete Convolution Transformation" Fractal and Fractional 7, no. 5: 402. https://doi.org/10.3390/fractalfract7050402

APA Style

Chen, T. (2023). Fractional-Order Accumulative Generation with Discrete Convolution Transformation. Fractal and Fractional, 7(5), 402. https://doi.org/10.3390/fractalfract7050402

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