A new representation for the solution of the Richards-type fractional differential equation

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-12 DOI:10.1002/mma.10394

Iz-iddine EL-Fassi, Juan J. Nieto, Masakazu Onitsuka

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引用次数: 0

Abstract

Richards in [35] proposed a modification of the logistic model to model growth of biological populations. In this paper, we give a new representation (or characterization) of the solution to the Richards-type fractional differential equation $D^{α} y (t) = y (t) \cdot (1 + a (t) y^{β} (t))$ for $t \geq 0$ , where $a : [0, \infty) \to ℝ$ is a continuously differentiable function on $[0, \infty), α \in (0,1)$ and $β$ is a positive real constant. The obtained representation of the solution can be used effectively for computational and analytic purposes. This study improves and generalizes the results obtained on fractional logistic ordinary differential equation.

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理查兹型分数微分方程解法的新表示法

理查兹在文献[35]中提出了对逻辑模型的修改，以模拟生物种群的增长。在本文中，我们给出了理查兹型分式微分方程解的新表示（或表征），其中，为连续可微分函数，为正实数常数。所获得的解的表示可以有效地用于计算和分析目的。这项研究改进并推广了分式逻辑常微分方程的研究成果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.