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Fractional Integrals and Derivatives: "True" versus "False"

This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional op...

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Médium: Online
Jazyk:angličtina
Vydáno: MDPI - Multidisciplinary Digital Publishing Institute 2021
Témata:
fractional derivatives
fractional integrals
fractional calculus
fractional anti-derivatives
fractional operators
integral transforms
convergent series
fractional integral
fractional derivative
numerical approximation
translation operator
distributed lag
time delay
scaling
dilation
memory
depreciation
probability distribution
fractional models
fractional differentiation
distributed time delay systems
Volterra equation
adsorption
fractional differential equations
numerical methods
smoothness assumptions
persistent memory
initial values
existence
uniqueness
Crank–Nicolson scheme
weighted Shifted Grünwald–Letnikov approximation
space fractional convection-diffusion model
stability analysis
convergence order
Caputo–Fabrizio operator
Atangana–Baleanu operator
fractional falculus
general fractional derivative
general fractional integral
Sonine condition
fractional relaxation equation
fractional diffusion equation
Cauchy problem
initial-boundary-value problem
inverse problem
fractional calculus operators
special functions
generalized hypergeometric functions
integral transforms of special functions
thema EDItEUR::G Reference, Information and Interdisciplinary subjects::GP Research and information: general
thema EDItEUR::P Mathematics and Science
On-line přístup:ONIX_20210501_9783036504940_221
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Shrnutí:This Special Issue is devoted to some serious problems that the Fractional Calculus (FC) is currently confronted with and aims at providing some answers to the questions like “What are the fractional integrals and derivatives?”, “What are their decisive mathematical properties?”, “What fractional operators make sense in applications and why?’’, etc. In particular, the “new fractional derivatives and integrals” and the models with these fractional order operators are critically addressed. The Special Issue contains both the surveys and the research contributions. A part of the articles deals with foundations of FC that are considered from the viewpoints of the pure and applied mathematics, and the system theory. Another part of the Special issue addresses the applications of the FC operators and the fractional differential equations. Several articles devoted to the numerical treatment of the FC operators and the fractional differential equations complete the Special Issue.

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