Reprint
Fractional Calculus: Theory and Applications
Edited by
September 2018
208 pages
- ISBN978-3-03897-206-8 (Paperback)
- ISBN978-3-03897-207-5 (PDF)
This book is a reprint of the Special Issue Fractional Calculus: Theory and Applications that was published in
Computer Science & Mathematics
Engineering
Physical Sciences
Public Health & Healthcare
Summary
Fractional calculus is allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons). It can be considered a branch of mathematical physics that deals with integro-differential equations, where integrals are of convolution type and exhibit mainly singular kernels of power law or logarithm type.It is a subject that has gained considerably popularity and importance in the past few decades in diverse fields of science and engineering. Efficient analytical and numerical methods have been developed but still need particular attention.The purpose of this Special Issue is to establish a collection of articles that reflect the latest mathematical and conceptual developments in the field of fractional calculus and explore the scope for applications in applied sciences.
Format
- Paperback
License
© 2019 by the authors; CC BY license
Keywords
generalized Langevin equation; regularized Prabhakar derivative; tempered memory kernel; Mittag-Leffler functions; free electron laser (FEL); Volterra equations; iterative solutions; Hermite polynomials; Legendre polynomials; multi-dimensional diffusion-wave equation; neutral-fractional diffusion-wave equation; fundamental solution; Mellin-Barnes integral; integral representation; Wright function; generalized Wright function; functional differential equations; fractional calculus; iterative procedures; fractional integrals and derivatives; Grünwald–Letnikov approach; Marchaud approach; fractional differences; Hadamard finite part; Hadamard fractional derivatives; COM-Poisson distributions; Modified Mittag–Leffler functions; fractional partial differential equations (fPDEs); discrete fracture networks (DFNs); anomalous transport; fractional advection-dispersion equations; fractional derivatives; Grünwald–Letnikov derivative; Weyl derivative; Marchaud derivative; fractional Laplace operator; extension operator; fractional differential equations; multiterm differential equations; Mittag–Leffler function; matrix function; fractional calculus; Caputo fractional derivatives; Mittag–Leffler functions; anomalous relaxation; near-earth objects; potentially hazardous asteroids; radial velocity determination; real-time measurements; differential filter; fractional derivative; approximate integration; exponential series; Prabhakar viscoelasticity; Q-factor; fractional calculus; Mittag-Leffler functions; Prabhakar function; Integral transforms; fractional differential equations (FDEs); numerical methods; multi-order systems (MOSs); multi-term equations; product integration (PI); fractional linear multi-step methods (FLMMs); MATLAB routines; pulsed-field gradient (PFG) anomalous diffusion; fractional derivative; nuclear magnetic resonance (NMR); magnetic resonance imaging (MRI); n/a