General Fractional Derivatives with Applications in Viscoelasticity

Dr. Xiao-Jun Yang is a full professor of China University of Mining and Technology, China. He was awarded the 2019 Obada-Prize, the Young Scientist Prize (Turkey), and Springer's Distinguished Researcher Award. His scientific interests include: Viscoelasticity, Mathematical Physics, Fractional Calculus and Applications, Fractals, Analytic Number Theory, and Special Functions. He has published over 160 journal articles and 4 monographs, 1 edited volume, and 10 chapters. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Methods in the Applied Sciences, Mathematical Modelling and Analysis, Journal of Thermal Stresses, and Thermal Science, and an associate editor of Journal of Thermal Analysis and Calorimetry, Alexandria Engineering Journal, and IEEE Access. Dr. Feng Gao is the associated dean and the leading professor of State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology. He is the recipient of the State Natural Science Award and the State Science and Technology Award. He has published over 280 scientific papers in the field of nonlinear mechanics, rock mechanics and underground engineering. He also serves as the PI or Co-PI of the National Key Research and Development Program of China, the National 973 Project, the funding of National Natural Science Foundation of China, the National Science and Technology Innovation Project, and the Research Innovation Group Project of the Ministry of Education. Dr. Yang Ju is Vice Director of State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing, China. He is the Cheung Kong Distinguished Professor of Geomechanics in Mining, Petroleum and Geotechnical Engineering. His current research interests include Fractal Geometry and Applications in Mining, Petroleum and Geotechnical Engineering, Transparentization and Visualization Methods for Discontinuous Structures and Stress Field of Rock Masses, and Transparentization and Prediction Methods for Rock Disasters.

• 1. Special Functions2. Fractional Derivatives with Singular Kernels3. Fractional Derivatives with Nonsingular Kernels4. Variable-order Fractional Derivatives with Singular Kernels5. Variable-order Fractional Derivatives with Nonsingular Kernels6. General derivatives7. Applications of Fractional-order Viscoelastic Models

"The book can be useful as a consulting text for definitions and references, which has a relative value in this internet-based open-access era. The naive reader will have to seek mathematical or physically based motivation elsewhere." --zbMATH Open"From the list it is obvious that it was not possible for the authors to list detailed properties, or the spaces of functions where the listed derivatives can be used. Also there are no proofs of the theorems stated. In this respect the book may be viewed as a handbook of various definitions of fractional derivatives. We stress that a rather large part of the book is devoted to fractional derivatives of variable order. Applications of fractional calculus in visco-elasticity are presented in the last chapter. The presentation is brief and shows the main results from the creep and stress relaxation experiments in linear visco-elasticity of fractional type.Having this in mind, we can say that the present book is suited for students and researchers in the field of fractional calculus who are interested in new contributions to the field. For more properties of the fractional derivatives listed in the book, the reader must consult the original references, given in the well-prepared reference list." --Mathematical Reviews Clippings, March 2022