Towards Ulam Type Multi Stability Analysis: A Novel Approach for Fuzzy Dynamical Systems
暫譯: 朝向烏拉姆型多穩定性分析：模糊動態系統的新穎方法

Rezaei Aderyani, Safoura, Saadati, Reza, Li, Chenkuan

Towards Ulam Type Multi Stability Analysis: A Novel Approach for Fuzzy Dynamical Systems
  • 出版商: Springer
  • 出版日期: 2025-05-17
  • 售價: $5,880
  • 貴賓價: 9.5 折 $5,586
  • 語言: 英文
  • 頁數: 571
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303155566X
  • ISBN-13: 9783031555664

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

The main target of this book is to present a new concept of Ulam-type stability, i.e., multi-stability, through the classical, well-known special functions and to obtain the best approximation error estimates by a different concept of perturbation stability including fuzzy approaches for uncertainty considerations. This stability allows us to obtain diverse approximations depending on various special functions that are initially chosen and to evaluate maximal stability and minimal error which enable us to obtain a unique optimal solution of functional equations, inequalities, and fractional equations. Stability analysis in the sense of the Ulam and its different kinds has received considerable attention from the researchers. However, how to effectively generalize the Ulam stability problems and to evaluate optimized controllability and stability are new issues. The multi-stability not only covers the previous concepts but also considers the optimization of the problem and provides a comprehensive discussion of optimizing the different types of the Ulam stabilities of mathematical models used in the natural sciences and engineering disciplines with fuzzy attitudes. Besides, this book also deals with nonlinear differential equations with various boundary conditions or initial value problems, based on the matrix Mittag-Leffler function, fixed point theory, as well as Babenko's approach to study uniqueness and existence of solutions. In general, the benefits for the readers can be concluded as follows:
1. Evaluates maximal stability with minimal error to get a unique optimal solution.
2. Discusses an optimal method of the alternative to study existence, uniqueness, and different types of Ulam stabilities under special consideration of the fuzzy approaches.
3. Delves into the new study of boundary value problems of fractional integro-differential equations with integral boundary conditions and variable coefficients.

商品描述(中文翻譯)

本書的主要目標是通過經典的、眾所周知的特殊函數，提出一種新的 Ulam 類型穩定性概念，即多重穩定性，並通過不同的擾動穩定性概念，包括模糊方法來考慮不確定性，獲得最佳近似誤差估計。這種穩定性使我們能夠根據最初選擇的各種特殊函數獲得多樣的近似，並評估最大穩定性和最小誤差，從而使我們能夠獲得功能方程、不等式和分數方程的唯一最優解。Ulam 的穩定性分析及其不同類型已受到研究人員的相當關注。然而，如何有效地概括 Ulam 穩定性問題以及評估優化的可控性和穩定性是新的課題。多重穩定性不僅涵蓋了先前的概念，還考慮了問題的優化，並提供了對於在自然科學和工程學科中使用的數學模型的不同類型 Ulam 穩定性的優化的全面討論，並採用模糊態度。此外，本書還處理具有各種邊界條件或初值問題的非線性微分方程，基於矩陣 Mittag-Leffler 函數、固定點理論以及 Babenko 的方法來研究解的唯一性和存在性。總體而言，對讀者的好處可以總結如下：
1. 評估最大穩定性與最小誤差以獲得唯一最優解。
2. 討論替代的最佳方法，以研究在特殊考慮模糊方法下的存在性、唯一性和不同類型的 Ulam 穩定性。
3. 深入研究具有積分邊界條件和變係數的分數積分微分方程的邊界值問題的新研究。

作者簡介

Tofigh Allahviranloo is a full professor of applied mathematics at Istinye University in Turkey and the Islamic Azad University (IAU) Science and Research Branch in Iran. He has previously worked at several universities, including the University of Prince Edward Island in Canada, Izmir University, and Bahcesehir University in Turkey.

As a mathematician and computer scientist, Prof. Allahviranloo is passionate about multi- and interdisciplinary research. He specializes in fundamental research in fuzzy applied mathematics, particularly fuzzy differential equations, and is focused on innovative applications in applied biological sciences. Currently, he is developing a new mathematical space to address complex uncertainties and is defining a new concept of uncertainty.

Safoura Rezaei Aderyani is a Ph.D. student in Mathematics at the Iran University of Science and Technology. She has extensively published papers on Ulam's type stability, including studies on difference, differential, functional, and integral equations. Her work also explores the applications of Ulam's type stability and its connections to other mathematical areas. Additionally, Rezaei Aderyani has contributed as an editor to several papers and special volumes focused on these subjects.

Reza Saadati is a faculty member at the Department of mathematics, Iran University of Science and Technology, in Iran. Dr. Saadati has authored over 5 international books and approximately 280 papers published by renowned publishers like Elsevier, Springer, and Wiley. He is the editor of several well-known journals such as Iran J Fuzzy System and fixed point theory and algorithms for Sci. and Eng-Springer.

Chenkuan Li has been a full professor at the Department of Mathematics and Computer Science since 2006. His research activities are devoted to distribution theory, generalized integral transforms, fractional analysis, and nonlinear differential equations with fixed point theory. He has published over 100 papers and has been supported by the Natural Sciences and Engineering Research Council of Canada for a long time. In addition, he was awarded the Brandon University Senate Award for Excellence in Research 2015 and Teaching in 2016.

作者簡介(中文翻譯)

Tofigh Allahviranloo 是土耳其 Istinye 大學及伊朗伊斯蘭阿茲哈大學（IAU）科學與研究分校的應用數學全職教授。他曾在多所大學任教，包括加拿大的愛德華王子島大學、土耳其的伊茲密爾大學和巴哈切希爾大學。

作為數學家和計算機科學家，Allahviranloo 教授對多學科及跨學科研究充滿熱情。他專注於模糊應用數學的基礎研究，特別是模糊微分方程，並致力於在應用生物科學中的創新應用。目前，他正在開發一個新的數學空間，以應對複雜的不確定性，並定義一個新的不確定性概念。

Safoura Rezaei Aderyani 是伊朗科學與技術大學的數學博士生。她在 Ulam 類型穩定性方面發表了大量論文，包括對差分方程、微分方程、函數方程和積分方程的研究。她的工作還探討了 Ulam 類型穩定性的應用及其與其他數學領域的聯繫。此外，Rezaei Aderyani 還作為編輯參與了多篇專注於這些主題的論文和專刊的編輯工作。

Reza Saadati 是伊朗科學與技術大學數學系的教職員。Saadati 博士已出版超過 5 本國際書籍，並在知名出版社如 Elsevier、Springer 和 Wiley 發表了約 280 篇論文。他是幾本知名期刊的編輯，如《Iran J Fuzzy System》和《固定點理論與科學與工程的算法 - Springer》。

Chenkuan Li 自 2006 年以來一直擔任數學與計算機科學系的全職教授。他的研究活動專注於分佈理論、廣義積分變換、分數分析以及帶有固定點理論的非線性微分方程。他已發表超過 100 篇論文，並長期獲得加拿大自然科學與工程研究委員會的支持。此外，他於 2015 年獲得布蘭登大學研究卓越獎，並於 2016 年獲得教學卓越獎。

類似商品