General Fractional Derivatives Theory, Methods and Applications
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.
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.