This book explores analytical and numerical approximate solutions obtained by operational matrix-based methods for both classical and fractional order differential equations. An important focus of the book is to develop operational matrix methods for solving problems of ship dynamical models and fractional order ship roll motion equations arising in ocean engineering. Also, this book provides comprehensive information on the conceptual basis of operational matrix theory and its applications. It provides an essential balance between mathematical rigor and the practical applications of operational matrix theory. The book is divided into 8 chapters. The first three chapters are devoted to the mathematical foundations and basics of operational matrix algorithms. The remaining chapters provide the machine learning-based operational matrix algorithms for linear, nonlinear and fractional ship dynamical problems. The book is ideally suited as a text for graduate, postgraduate and research students in applied mathematics and computing.

Dr. G. Hariharan is Professor of mathematics at the School of Arts, Sciences, Humanities and Education (SASHE), SASTRA Deemed University, Thanjavur, India. He obtained his Ph.D. in applied mathematics and has over two decades of teaching and research experience in the areas of numerical analysis, computational methods, and nonlinear differential equations. His research contributions span scientific computing, fractional and nonlinear dynamical models, and wavelet-based computational techniques. Dr. Hariharan has authored more than 110 research papers in reputed SCI-indexed international journals and contributed book chapters to leading publishers such as Springer and Elsevier. He has successfully completed several national and international research projects, including collaborations under DST-SERB and SPARC programs, and maintains active partnerships with global institutions such as the University of Alberta (Canada) and the University of South Africa (UNISA).

Prof. Bin Han is Distinguished Professor of mathematical sciences in the Department of Mathematical and Statistical Sciences, University of Alberta, Canada, widely recognized for his pioneering contributions to applied and computational harmonic analysis, wavelet theory, and framelet constructions. A leading authority in the field of modern mathematical analysis, Prof. Han’s research bridges pure and applied mathematics with deep implications in signal processing, image analysis, and data science. He earned his Ph.D. in mathematics from the University of Alberta and has since built an exceptional academic career characterized by scholarly excellence, innovation, and mentorship. Prof. Han’s research focuses on wavelets, frames, subdivision schemes, and multiresolution analysis, developing elegant mathematical tools with real-world applications in engineering, imaging, and computational modeling.

Prof. Hossein Jafari is Distinguished Professor of mathematical sciences at the University of South Africa (UNISA), renowned internationally for his pioneering contributions to applied mathematics, fractional calculus, and nonlinear dynamical systems. With a prolific academic career spanning over two decades, Prof. Jafari has established himself as Leading Researcher, Educator, and Collaborator in the global mathematical community. He obtained his Ph.D. in applied mathematics from a reputed university and began his career with a strong focus on analytical and numerical methods for solving fractional differential equations. His research interests include homotopy analysis methods, wavelet approaches, differential equations in engineering and physics, and fractional order models in complex systems.