Frontiers of Fractal Analysis: Recent Advances and Challenges

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems.

This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

描述自然物體使用幾何形狀的歷史可以追溯到科學本身的出現，傳統形狀是我們對幾何的直觀理解的基礎。然而，自然界並不僅限於這些通常由整數維度特徵化的歐幾里德物體。因此，傳統的幾何方法無法滿足解決或分析與自然現象相關的非線性問題的要求，因此，分形理論應運而生，旨在理解複雜性並提供一種識別不規則性和複雜系統的創新方式。儘管分形幾何的概念在科學、工程和社會問題的許多前沿領域中得到了廣泛應用，但它們對於傳統科學領域也具有更實際的有趣含義。自其發現以來，使用這一強大概念在幾乎每個科學學科的各個分支中進行了大量的研究活動，以深入瞭解許多未解決的問題。

本書包括八章，重點是收集尖端研究並提出在傳統科學學科和應用領域中應用分形特徵的方法。

Santo Banerjee is associated with the Department of Mathematics, Politecnico di Torino, Italy. Prior to this, he was an Associate Professor in the Institute for Mathematical Research (INSPEM), University Putra Malaysia, Malaysia, until 2020, and also a founder member of the Malaysia-Italy Centre of Excellence in Mathematical Science, UPM, Malaysia. His research is mainly concerned with Nonlinear Dynamics, Chaos, Complexity and Secure Communication. He is a Managing Editor of EPJ Plus (Springer).

A. Gowrisankar has a master's degree and Ph.D in Mathematics from The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Dindigul, India, in 2012 and 2017 respectively. He got an institute postdoctoral fellowship from the Indian Institute of Technology Guwahati (IITG), Guwahati, Assam, India, in 2017. At present, he is an Assistant Professor in the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India. His broad areas of research include Fractal Analysis, Image Processing, Fractional Calculus and Fractal Functions.

Santo Banerjee是義大利都靈理工大學數學系的成員。在此之前，他是馬來西亞大學Putra的數學研究所（INSPEM）的副教授，直到2020年，也是馬來西亞大學Putra的馬來西亞-義大利數學科學卓越中心的創始成員。他的研究主要涉及非線性動力學、混沌、複雜性和安全通信。他是Springer出版社的《EPJ Plus》的總編輯。

A. Gowrisankar於2012年和2017年分別在印度甘地格蘭鄉村學院（被視為大學）獲得數學碩士學位和博士學位。他於2017年獲得印度古瓦哈提印度理工學院（IITG）的研究所博士後獎學金。目前，他是印度泰米爾納德邦維特羅高等科學學院高等科學學院數學系的助理教授。他的研究範圍包括分形分析、影像處理、分數微積分和分形函數。