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This book addresses different applied problems in order to demonstrate the feasibility of fractional calculus’ use, irrespective of the type of memory kernels used, to model varieties of natural phenomena and new processes emerging in advanced technologies. In this context, the book’s focus is on modelling, adequate results, and interpretations, rather than theorems and proofs. The book includes a total of 12 chapters, representing various aspects of applied fractional modelling and covering important issues in modern technologies to provide a better understanding of applications of fractional calculus in applied modelling. The book will be a versatile source of information for undergraduate and graduate students, and for scientists involved in modelling of nonlinear and hereditary phenomena.

Various numerical and analytical methods have been used to investigate the models of real-world phenomena. Namely, real-world models from quantum physics have been investigated by many researchers. This Research Topic aims to promote and exchange new and important theoretical and numerical results to study the dynamics of complex physical systems. In particular, the Research Topic will focus on numerical and analytical methods for nonlinear partial differential equations which have applications for quantum physical systems. Authors are encouraged to introduce their latest original research articles. The Research Topic will cover, but is not limited to, the following themes: - Mathematical methods in physics - Representations of Lie groups in physics - Quantum fields - Advanced numerical methods and techniques for nonlinear partial differential equations - Schrödinger classical and fractional operators - Conservation laws

Second International Conference on Emerging Trends in IOT and Computing Technologies (ICEICT – 2023) is organised with a vision to address the various issues to promote the creation of intelligent solution for the future. It is expected that researchers will bring new prospects for collaboration across disciplines and gain ideas facilitating novel concepts. Second International Conference of Emerging Trends in IoT and Computer Technologies (ICEICT-2023) is an inventive event organised in Goel Institute of Technology and Management, Lucknow, India, with motive to make available an open International forum for the researches, academicians, technocrats, scientist, engineers, industrialist and students around the globe to exchange their innovations and share the research outcomes which may lead the young researchers, academicians and industrialist to contribute to the global society. The conference ICEICT- 2023 is being organised at Goel Institute of Technology and Management, Lucknow, Uttar Pradesh, during 12-13 January 2024. It will feature world-class keynote speakers, special sessions, along with the regular/oral paper presentations. The conference welcomes paper submissions from researcher, practitioners, academicians and students will cover numerous tracks in the field of Computer Science and Engineering and associated research areas.

Traditional models struggle to cope with complexity, noise, and the existence of a changing environment, while Computational Intelligence (CI) offers solutions to complicated problems as well as reverse problems. The main feature of CI is adaptability, spanning the fields of machine learning and computational neuroscience. CI also comprises biologically-inspired technologies such as the intellect of swarm as part of evolutionary computation and encompassing wider areas such as image processing, data collection, and natural language processing. This book aims to discuss the usage of CI for optimal solving of various applications proving its wide reach and relevance. Bounding of optimization methods and data mining strategies make a strong and reliable prediction tool for handling real-life applications.

The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.

This book is devoted to the study of artificial intelligence from a new perspective – not just a technology but a social institution with complex social connections and relationships. The book systematically highlights technological trends of the artificial intelligence economy and considers all the components of its cascade effect with an overview of international experience and substantiation of promising ways of adapting to the modern stage of technological transit of economic systems. The cascade effect is understood as a chain of interdependent events that are triggered as artificial intelligence takes root in society and the economy. Among the technological trends (current areas of the practical application of artificial intelligence), highlighted in the book, are “smart” homes, digital regions, the use of artificial intelligence to ensure cybersecurity, as well as the optimization of business processes based on artificial intelligence. The book interprets the economics of artificial intelligence as a result of the transition to a digital technological order. A review of modern experience and regulatory perspectives of the institutionalization of the artificial intelligence economy is carried out. The legal framework for combating cyber threats in the artificial intelligence economy has been determined. The promising frameworks for using artificial intelligence in various branches of industry are presented. The book provides practical examples, case studies and proposed frameworks for using AI in various sectors of the economy, which allows using the book as a practical guide to managing the artificial intelligence economy.

Recent Trends in Fractional Calculus and Its Applications addresses the answer to this very basic question: "Why is Fractional Calculus important?" Until recent times, Fractional Calculus was considered as a rather esoteric mathematical theory without applications, but in the last few decades there has been an explosion of research activities on the application of Fractional Calculus to very diverse scientific fields ranging from the physics of diffusion and advection phenomena, to control systems to finance and economics. An important part of mathematical modelling of objects and processes is a description of their dynamics.The term Fractional Calculus is more than 300 years old. It is a generalization of the ordinary differentiation and integration to noninteger (arbitrary) order. The subject is as old as the calculus of differentiation and goes back to times when Leibniz, Gauss, and Newton invented this kind of calculation. Several mathematicians contributed to this subject over the years. People like Liouville, Riemann, and Weyl made major contributions to the theory of Fractional Calculus. In recent decades the field of Fractional Calculus has attracted the interest of researchers in several areas, including mathematics, physics, chemistry, engineering, finance, and social sciences. - Provides the most recent and up-to-date developments in the Fractional Calculus and its application areas - Presents pre-preparation ideas to help researchers/scientists/clinicians face the new challenges in the application of fractional differential equations - Helps researchers and scientists understand the importance of the Fractional Calculus to solve many problems in Biomedical Engineering and applied sciences

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.