General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science.
- Give some new results for fractional calculus of constant and variable orders.
- Discuss some new definitions for fractional calculus with respect to another function.
- Provide definitions for general fractional calculus of constant and variable orders.
- Report new results of general fractional calculus with respect to another function.
- Propose news special functions with respect to another function and their applications.
- Present new models for the anomalous relaxation and rheological behaviors.
This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students.
Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.
Table of Contents
Introduction. Fractional Derivatives of Constant Order and Applications. General Fractional Derivatives of Constant Order and Applications. Fractional Derivatives of Variable Order and Applications. Fractional Derivatives of Variable Order with Respect to Another Function and Applications. A Laplace Transforms of the functions. B Fourier Transforms of the functions. C Mellin transforms of the functions. D The special functions and their expansions. Bibliography. Index.
Dr. Xiao-Jun Yang is a full Professor of Applied Mathematics and Mechanic, at State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, China. His scientific interests include: Viscoelasticity, Nonlinear Dynamics, Mathematical Physics, Analytical, Approximate, Numerical and Exact Solutions for ODEs and PDEs, Integral Transforms and Their Applications, Continuous Mechanics,Rock mechanics, Fluid Mechanics, Heat Transfer, and Traffic Flow, Wavelets, Signal Processing, Biomathematics, General Calculus and Applications, Fractional Calculus and Applications, Local Fractional Calculus and Applications, General Fractional Calculus and Applications, Variable Order Fractional Calculus and Applications and Variable Order Fractional Calculus with Respect to Another Function and Applications. He has published over 160 journal articles and 5 books, as well as monographs, and edited volumes and 10 chapters. In 2017 and 2018, he was awarded the Elsevier Most Cited Chinese Researchers in Mathematics and the 2017 Chinese 100 Best Impact International Academic Paper. In 2018, he was selected as one of the "333" Program Talents of Jiangsu Province, China. He is currently an editor of several scientific journals, such as Fractals-Complex Geometry, Patterns, and Scaling in Nature and Society, Mathematical Methods in the Applied Sciences, Applied Numerical Mathematics, International Journal of Numerical Methods for Heat & Fluid Flow, Mathematical Modelling and Analysis, and Thermal Science. He is also the referee of articles and books from Springer Nature, Elsevier, World Scientific and CRC Press publishers.