LEADER 04767nam 2200937z- 450 001 9910566459803321 005 20220506 035 $a(CKB)5680000000037783 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/80975 035 $a(oapen)doab80975 035 $a(EXLCZ)995680000000037783 100 $a20202205d2022 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 00$aFractional Calculus and Special Functions with Applications 210 $aBasel$cMDPI - Multidisciplinary Digital Publishing Institute$d2022 215 $a1 online resource (164 p.) 311 08$a3-0365-3617-5 311 08$a3-0365-3618-3 330 $aThe study of fractional integrals and fractional derivatives has a long history, and they have many real-world applications because of their properties of interpolation between integer-order operators. This field includes classical fractional operators such as Riemann-Liouville, Weyl, Caputo, and Grunwald-Letnikov; nevertheless, especially in the last two decades, many new operators have also appeared that often define using integrals with special functions in the kernel, such as Atangana-Baleanu, Prabhakar, Marichev-Saigo-Maeda, and the tempered fractional equation, as well as their extended or multivariable forms. These have been intensively studied because they can also be useful in modelling and analysing real-world processes, due to their different properties and behaviours from those of the classical cases.Special functions, such as Mittag-Leffler functions, hypergeometric functions, Fox's H-functions, Wright functions, and Bessel and hyper-Bessel functions, also have important connections with fractional calculus. Some of them, such as the Mittag-Leffler function and its generalisations, appear naturally as solutions of fractional differential equations. Furthermore, many interesting relationships between different special functions are found by using the operators of fractional calculus. Certain special functions have also been applied to analyse the qualitative properties of fractional differential equations, e.g., the concept of Mittag-Leffler stability.The aim of this reprint is to explore and highlight the diverse connections between fractional calculus and special functions, and their associated applications. 606 $aMathematics & science$2bicssc 606 $aResearch & information: general$2bicssc 610 $aAbel equations 610 $aanalytic continuation 610 $aAppell functions 610 $aAtangana-Baleanu derivative 610 $aAtangana-Baleanu fractional calculus 610 $aboundary conditions 610 $acalculus of variations 610 $aCaputo-Hadamard fractional derivative 610 $acomplex integrals 610 $acoupled system 610 $aelectrical circuits 610 $aerror bound 610 $aexistence 610 $aexistence and uniqueness solution 610 $afixed point theorem 610 $afixed point theory 610 $afractional derivative 610 $afractional derivatives 610 $afractional derivatives and integrals 610 $afractional differential equations 610 $afractional integrals 610 $afractional Langevin equations 610 $afractional modeling 610 $afractional-order Caputo derivative operator 610 $afractional-order Riemann-Liouville integral operator 610 $agenerating function 610 $aHadamard fractional integral 610 $ahypergeometric function 610 $aintegral representation 610 $ak-beta function 610 $ak-gamma function 610 $aLaplace transforms 610 $aMittag-Leffler functions 610 $amixed partial derivatives 610 $amobile phone worms 610 $an/a 610 $aphysical problems 610 $aPochhammer symbol 610 $aPrabhakar fractional calculus 610 $areal-world problems 610 $areduction and transformation formula 610 $asecond Chebyshev wavelet 610 $astochastic processes 610 $asystem of Volterra-Fredholm integro-differential equations 615 7$aMathematics & science 615 7$aResearch & information: general 700 $aO?zarslan$b Mehmet Ali$4edt$01326288 702 $aFernandez$b Arran$4edt 702 $aArea$b Ivan$4edt 702 $aO?zarslan$b Mehmet Ali$4oth 702 $aFernandez$b Arran$4oth 702 $aArea$b Ivan$4oth 906 $aBOOK 912 $a9910566459803321 996 $aFractional Calculus and Special Functions with Applications$93037268 997 $aUNINA