Reprint

Operators of Fractional Calculus and Their Applications

Edited by
January 2019
136 pages
  • ISBN978-3-03897-340-9 (Paperback)
  • ISBN978-3-03897-341-6 (PDF)

This book is a reprint of the Special Issue Operators of Fractional Calculus and Their Applications that was published in

Computer Science & Mathematics
Engineering
Physical Sciences
Public Health & Healthcare
Summary

During the past four decades or so, various operators of fractional calculus, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdelyi–Kober, Liouville–Caputo, and so on, have been found to be remarkably popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integro-differential equations, together with the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.

Format
  • Paperback
License
© 2019 by the authors; CC BY-NC-ND license
Keywords
system of nonlinear fractional partial differential equations (NFPDEs); systems of nonlinear wave equations; new analytical technique (NAT); existence theorem; error analysis; approximate solution; stability; monomial functional equation; direct method; numerical partial differential equations (PDEs); radial basis function-finite difference (RBF-FD) method; ghost node; preconditioning; regularization; floating point arithmetic; fractional differential equations (FDEs); Lyapunov exponent; stability; Green’s function; distribution theory; particular solution; Kummer’s differential equation; hypergeometric differential equation; Laplace transform; n/a; distribution; fractional calculus; convolution; series convergence; Laplace transform; Gamma function; Mittag–Leffler function; distribution; fractional calculus; convolution; Abel’s integral equation; product; Mittag-Leffler function; α-admissible mapping; α-admissible; F-contraction; α-F-convex contraction; fixed point; non-linear Fredholm integral equation; n/a