General Fractional Derivatives: Theory, Methods and Applications, 1st Edition (Hardback) book cover

General Fractional Derivatives

Theory, Methods and Applications, 1st Edition

By Xiao-Jun Yang

Chapman and Hall/CRC

384 pages | 32 B/W Illus.

Purchasing Options:$ = USD
Hardback: 9781138336162
pub: 2019-06-05
SAVE ~$22.49
Available for pre-order
$149.95
$127.46
x


FREE Standard Shipping!

Description

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.

Features:

  • 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.

About the Author

Xiao-Jun Yang is a member of the Institute for Chinese Institute of Electronics and the Chinese Society of Theoretical and Applied Mechanics. His research interests are in the areas of fractal mathematics (Geometry, applied mathematics and functional analysis), fractal Mechanics (fractal elasticity and fractal fracture mechanics, fractal rock mechanics and fractional continuous mechanics in fractal media), fractional calculus and its applications, fractional differential equation, fractal differential equations of applied mathematics, local fractional differential equation, local fractional integral transforms, local fractional short-time analysis and wavelet analysis, local fractional functional analysis, local fractional calculus and its application. His academic contribution is one of founders of local fractional calculus of real and complex functions, local fractional Fourier analysis, fast Yang-Fourier transforms, local fractional calculus of complex functions, Yang-Fourier and Yang-Laplace transforms, local fractional functional analysis, local fractional short-time and wavelet transforms and discrete Yang-Fourier transforms.

Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT004000
MATHEMATICS / Arithmetic
MAT007000
MATHEMATICS / Differential Equations