TY - BOOK ID - 138666127 TI - Fractional Integrals and Derivatives: "True" versus "False" PY - 2021 PB - Basel, Switzerland MDPI - Multidisciplinary Digital Publishing Institute DB - UniCat KW - fractional derivatives KW - fractional integrals KW - fractional calculus KW - fractional anti-derivatives KW - fractional operators KW - integral transforms KW - convergent series KW - fractional integral KW - fractional derivative KW - numerical approximation KW - translation operator KW - distributed lag KW - time delay KW - scaling KW - dilation KW - memory KW - depreciation KW - probability distribution KW - fractional models KW - fractional differentiation KW - distributed time delay systems KW - Volterra equation KW - adsorption KW - fractional differential equations KW - numerical methods KW - smoothness assumptions KW - persistent memory KW - initial values KW - existence KW - uniqueness KW - Crank–Nicolson scheme KW - weighted Shifted Grünwald–Letnikov approximation KW - space fractional convection-diffusion model KW - stability analysis KW - convergence order KW - Caputo–Fabrizio operator KW - Atangana–Baleanu operator KW - fractional falculus KW - general fractional derivative KW - general fractional integral KW - Sonine condition KW - fractional relaxation equation KW - fractional diffusion equation KW - Cauchy problem KW - initial-boundary-value problem KW - inverse problem KW - fractional calculus operators KW - special functions KW - generalized hypergeometric functions KW - integral transforms of special functions UR - https://www.unicat.be/uniCat?func=search&query=sysid:138666127 AB - 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. ER -