Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability
Abbas, Saïd, Ahmad, Bashir, Benchohra, Mouffak
- 出版商: Morgan Kaufmann
- 出版日期: 2024-01-16
- 售價: $6,280
- 貴賓價: 9.5 折 $5,966
- 語言: 英文
- 頁數: 300
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0443236011
- ISBN-13: 9780443236013
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商品描述
The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences.
商品描述(中文翻譯)
分數微積分(FC)領域已有超過300年的歷史,據說起源於1695年L'Hopital和Leibniz之間關於分數階導數的問題。這個數學分析的分支被視為傳統微積分的推廣,因為它處理分數階的導數和積分運算子。分數微積分的工具在改進許多自然現象和工程、社會、自然和生物醫學科學領域中的過程的數學建模方面非常有用。《分數差分、微分方程和包含:分析和穩定性》專注於多個類別的功能性分數差分方程和包含的解的存在和穩定性(Ulam-Hyers-Rassias穩定性和漸近穩定性)。一些方程包括有限、無限或狀態相依性的延遲效應。其他方程受到可能是固定或非即時的衝擊效應的影響。用於建立所提出問題的存在結果的工具包括不動點定理、密度技術、單調迭代技術、Ulam穩定性、吸引力和非緊緻性度量以及弱非緊緻性度量的概念。所有抽象結果都以應用數學、工程、生物醫學和其他應用科學的例子加以說明。