应用数学和分数阶微积分

English | PDF | 2022 | 440 Pages | ISBN : 3036551484 | 16.3 MB

In the last three decades, fractional calculus has broken into the field of mathematical analysis, both at the theoretical level and at the level of its applications. In essence, the fractional calculus theory is a mathematical analysis tool applied to the study of integrals and derivatives of arbitrary order, which unifies and generalizes the classical notions of differentiation and integration. These fractional and derivative integrals, which until not many years ago had been used in purely mathematical contexts, have been revealed as instruments with great potential to model problems in various scientific fields, such as: fluid mechanics, viscoelasticity, physics, biology, chemistry, dynamical systems, signal processing or entropy theory. Since the differential and integral operators of fractional order are nonlinear operators, fractional calculus theory provides a tool for modeling physical processes, which in many cases is more useful than classical formulations. This is why the application of fractional calculus theory has become a focus of international academic research. This Special Issue "Applied Mathematics and Fractional Calculus" has published excellent research studies in the field of applied mathematics and fractional calculus, authored by many well-known mathematicians and scientists from diverse countries worldwide such as China, USA, Canada, Germany, Mexico, Spain, Poland, Portugal, Iran, Tunisia, South Africa, Albania, Thailand, Iraq, Egypt, Italy, India, Russia, Pakistan, Taiwan, Korea, Turkey, and Saudi Arabia.

在过去的三十年里，分数 calculus 已经进入了数学分析的领域，在理论水平和应用水平上。本质上说，分数 calculus 理论是一种应用于研究任意阶积分和导数的数学分析工具，它将经典微分和积分的概念统一化和推广了。这些直到几年前还仅限于纯粹数学领域的分数和导数积分，被揭示为能够很好地建模各种科学领域中的问题的强大工具，如：流体力学、黏弹性、物理、生物学、化学、动态系统、信号处理或熵理论。由于分数阶的微分和积分运算器是非线性运算了，分数 calculus 理论提供了对许多情况下比经典形式更具实用性的建模物理过程的方法。这就是为什么应用分数 calculus 理论成为一个国际学术研究的重点。本特刊“应用数学与分数 calculus”发表了应用数学领域和分数 calculus 的优秀研究成果，由来自世界各地的众多著名数学家和科学家撰写的，包括中国、美国、加拿大、德国、墨西哥、西班牙、波兰、葡萄牙、伊朗、突尼斯、南非、阿尔巴尼亚、泰国、伊拉克、埃及、意大利、印度、俄罗斯、巴基斯坦、台湾、韩国、土耳其和沙特阿拉伯。

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