04102nam 2200949z- 450 991055771920332120231214133346.0(CKB)5400000000046132(oapen)https://directory.doabooks.org/handle/20.500.12854/68475(EXLCZ)99540000000004613220202105d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierFractional Integrals and Derivatives: "True" versus "False"Basel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20211 electronic resource (280 p.)3-0365-0494-X 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.Fractional Integrals and DerivativesResearch & information: generalbicsscMathematics & sciencebicsscfractional derivativesfractional integralsfractional calculusfractional anti-derivativesfractional operatorsintegral transformsconvergent seriesfractional integralfractional derivativenumerical approximationtranslation operatordistributed lagtime delayscalingdilationmemorydepreciationprobability distributionfractional modelsfractional differentiationdistributed time delay systemsVolterra equationadsorptionfractional differential equationsnumerical methodssmoothness assumptionspersistent memoryinitial valuesexistenceuniquenessCrank–Nicolson schemeweighted Shifted Grünwald–Letnikov approximationspace fractional convection-diffusion modelstability analysisconvergence orderCaputo–Fabrizio operatorAtangana–Baleanu operatorfractional falculusgeneral fractional derivativegeneral fractional integralSonine conditionfractional relaxation equationfractional diffusion equationCauchy probleminitial-boundary-value probleminverse problemfractional calculus operatorsspecial functionsgeneralized hypergeometric functionsintegral transforms of special functionsResearch & information: generalMathematics & scienceLuchko Yuriedt1280963Luchko YuriothBOOK9910557719203321Fractional Integrals and Derivatives: "True" versus "False"3017754UNINA