LEADER 04106nam 2200949z- 450 001 9910557719203321 005 20231214133346.0 035 $a(CKB)5400000000046132 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/68475 035 $a(EXLCZ)995400000000046132 100 $a20202105d2021 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFractional Integrals and Derivatives: "True" versus "False" 210 $aBasel, Switzerland$cMDPI - Multidisciplinary Digital Publishing Institute$d2021 215 $a1 electronic resource (280 p.) 311 $a3-0365-0494-X 330 $aThis 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. 517 $aFractional Integrals and Derivatives 606 $aResearch & information: general$2bicssc 606 $aMathematics & science$2bicssc 610 $afractional derivatives 610 $afractional integrals 610 $afractional calculus 610 $afractional anti-derivatives 610 $afractional operators 610 $aintegral transforms 610 $aconvergent series 610 $afractional integral 610 $afractional derivative 610 $anumerical approximation 610 $atranslation operator 610 $adistributed lag 610 $atime delay 610 $ascaling 610 $adilation 610 $amemory 610 $adepreciation 610 $aprobability distribution 610 $afractional models 610 $afractional differentiation 610 $adistributed time delay systems 610 $aVolterra equation 610 $aadsorption 610 $afractional differential equations 610 $anumerical methods 610 $asmoothness assumptions 610 $apersistent memory 610 $ainitial values 610 $aexistence 610 $auniqueness 610 $aCrank?Nicolson scheme 610 $aweighted Shifted Grünwald?Letnikov approximation 610 $aspace fractional convection-diffusion model 610 $astability analysis 610 $aconvergence order 610 $aCaputo?Fabrizio operator 610 $aAtangana?Baleanu operator 610 $afractional falculus 610 $ageneral fractional derivative 610 $ageneral fractional integral 610 $aSonine condition 610 $afractional relaxation equation 610 $afractional diffusion equation 610 $aCauchy problem 610 $ainitial-boundary-value problem 610 $ainverse problem 610 $afractional calculus operators 610 $aspecial functions 610 $ageneralized hypergeometric functions 610 $aintegral transforms of special functions 615 7$aResearch & information: general 615 7$aMathematics & science 700 $aLuchko$b Yuri$4edt$01280963 702 $aLuchko$b Yuri$4oth 906 $aBOOK 912 $a9910557719203321 996 $aFractional Integrals and Derivatives: "True" versus "False"$93017754 997 $aUNINA