04752nam 2201225z- 450 991061946180332120231214133008.03-0365-5368-1(CKB)5670000000391657(oapen)https://directory.doabooks.org/handle/20.500.12854/93243(EXLCZ)99567000000039165720202210d2022 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierFractional Calculus Operators and the Mittag-Leffler FunctionMDPI - Multidisciplinary Digital Publishing Institute20221 electronic resource (258 p.)3-0365-5367-3 This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others.Research & information: generalbicsscMathematics & sciencebicsscfractional derivativegeneralized Mittag-Leffler kernel (GMLK)Legendre polynomialsLegendre spectral collocation methoddynamical systemsrandom time changeinverse subordinatorasymptotic behaviorMittag-Leffler functiondata fittingmagnetizationmagnetic fluidsGamma functionPsi functionPochhammer symbolhypergeometric function 2F1generalized hypergeometric functions tFuGauss's summation theorem for 2F1(1)Kummer's summation theorem for 2F1(−1)generalized Kummer's summation theorem for 2F1(−1)Stirling numbers of the first kindHilfer-Hadamard fractional derivativeRiemann-Liouville fractional derivativeCaputo fractional derivativefractional differential equationsinclusionsnonlocal boundary conditionsexistence and uniquenessfixed pointgamma functionBeta functionMittag-Leffler functionGeneralized Mittag-Leffler functionsgeneralized hypergeometric functionFox-Wright functionrecurrence relationsRiemann-Liouville fractional calculus operators(α, h-m)-p-convex functionFejér-Hadamard inequalityextended generalized fractional integralsMittag-Leffler functionsinitial value problemsLaplace transformexact solutionChebyshev inequalityPólya-Szegö inequalityfractional integral operatorsWright functionSrivastava's polynomialsfractional calculus operatorsLavoie-Trottier integral formulaOberhettinger integral formulafractional partial differential equationboundary value problemseparation of variablesMittag-LefflerAbel-Gontscharoff Green's functionHermite-Hadamard inequalitiesconvex functionκ-Riemann-Liouville fractional integralDirichlet averagesB-splinesdirichlet splinesRiemann-Liouville fractional integralshypergeometric functions of one and several variablesgeneralized Mittag-Leffler type functionSrivastava-Daoust generalized Lauricella hypergeometric functionfractional calculusHermite-Hadamard inequalityFox H functionsubordinator and inverse stable subordinatorLamperti laworder statisticResearch & information: generalMathematics & scienceAndrić Majaedt1246427Andrić MajaothBOOK9910619461803321Fractional Calculus Operators and the Mittag-Leffler Function3038941UNINA