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Fractional Integrals and Derivatives: “True” versus “False”
Yuri Luchko (editor)
2021
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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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Keywords
- adsorption
- Atangana–Baleanu operator
- Caputo–Fabrizio operator
- Cauchy problem
- convergence order
- convergent series
- Crank–Nicolson scheme
- depreciation
- dilation
- distributed lag
- distributed time delay systems
- existence
- fractional anti-derivatives
- Fractional calculus
- fractional calculus operators
- fractional derivative
- fractional derivatives
- fractional differential equations
- fractional differentiation
- fractional diffusion equation
- fractional falculus
- fractional integral
- fractional integrals
- fractional models
- fractional operators
- fractional relaxation equation
- general fractional derivative
- general fractional integral
- generalized hypergeometric functions
- initial values
- initial-boundary-value problem
- Integral transforms
- integral transforms of special functions
- inverse problem
- Mathematics & science
- Memory
- numerical approximation
- Numerical methods
- Persistent Memory
- Probability Distribution
- Reference, information & interdisciplinary subjects
- Research & information: general
- scaling
- smoothness assumptions
- Sonine condition
- space fractional convection-diffusion model
- special functions
- stability analysis
- time delay
- translation operator
- Uniqueness
- Volterra equation
- weighted Shifted Grünwald–Letnikov approximation
Links
DOI: 10.3390/books978-3-0365-0494-0Editions