Bøker i Industrial and Applied Mathema-serien

This book contains select chapters on support vector algorithms from different perspectives, including mathematical background, properties of various kernel functions, and several applications. The main focus of this book is on orthogonal kernel functions, and the properties of the classical kernel functions¿Chebyshev, Legendre, Gegenbauer, and Jacobi¿are reviewed in some chapters. Moreover, the fractional form of these kernel functions is introduced in the same chapters, and for ease of use for these kernel functions, a tutorial on a Python package named ORSVM is presented. The book also exhibits a variety of applications for support vector algorithms, and in addition to the classification, these algorithms along with the introduced kernel functions are utilized for solving ordinary, partial, integro, and fractional differential equations.On the other hand, nowadays, the real-time and big data applications of support vector algorithms are growing. Consequently, the Compute Unified Device Architecture (CUDA) parallelizing the procedure of support vector algorithms based on orthogonal kernel functions is presented. The book sheds light on how to use support vector algorithms based on orthogonal kernel functions in different situations and gives a significant perspective to all machine learning and scientific machine learning researchers all around the world to utilize fractional orthogonal kernel functions in their pattern recognition or scientific computing problems.

This book collects select chapters on modern industrial problems related to uncertainties and vagueness in the expert domain of knowledge. The book further provides the knowledge related to application of various mathematical and statistical tools in these areas. The results presented in the book help the researchers and scientists in handling complicated projects in their domains. Useful to industrialists, academicians, researchers and students alike, the book aims to help managers and technical specialists in designing and implementation of reliability and risk programs as below: Ensure the system safety and risk informed asset management Follow a proper strategy to maintain the mechanical components of the system Schedule the proper actions throughout the product life cycle Understand the structure and cost of a complex system Plan the proper schedule to improve the reliability and life of the system Identify unwanted failures and set up preventive and correction action

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels. The book presents the dynamic of Covid-19 spread behaviour worldwide. It is noticed that the spread dynamic followed process with nonlocal behaviours which resemble power law, fading memory, crossover and stochastic behaviours. Fractional stochastic differential equations are therefore used to model spread behaviours in different parts of the worlds. The content coverage includes brief history of Covid-19 spread worldwide from December 2019 to September 2021, followed by statistical analysis of collected data for infected, death and recovery classes.

This is an introductory-level text on fractional calculus and fractional differential equations. Targeted to graduate students of mathematics and researchers, it contains several new definitions of fractional integrals and fractional derivatives. With interesting applications of the subject in several areas of physical sciences, life sciences, engineering, and technology, the book helps the students understand the importance and developments of this topic. The book is enriched with a list of useful references to published literature, and the presentation of the book is entirely new and easily comprehensible to the students. Some of the topics are refined, and new examples are included to supplement theories to help students understand the concepts easily and clearly.

This book deals with several types of multi-dimensional control problems in the face of data uncertainty for vector cases-multi-dimensional multi-objective control problem with uncertain objective functionals, uncertain constraint functionals, and uncertain objective as well as constraint functionals, uncertain multi-dimensional multi-objective control problem with semi-infinite constraints, uncertain dual multi-dimensional multi-objective variational control problem, and second-order PDE&PDI constrained robust optimization problem. The book provides the solution approaches-an exact l1 penalty function approach, modified objective approach, robust approach-in the simplest way to solve the recent developing optimization problems in the sense of uncertainty.