Fractional Calculus Operators and the Mittag-Leffler Function

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 gi...

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Médium:	E-kniha
Jazyk:	English
Vydavateľské údaje:	MDPI - Multidisciplinary Digital Publishing Institute 2022
Predmet:	Abel-Gontscharoff Green’s function asymptotic behavior B-splines Beta function boundary value problem Caputo fractional derivative Chebyshev inequality convex function data fitting Dirichlet averages dirichlet splines dynamical systems exact solution existence and uniqueness extended generalized fractional integrals Fejér–Hadamard inequality fixed point Fox H function Fox–Wright function fractional calculus fractional calculus operators fractional derivative fractional differential equations fractional integral operators fractional partial differential equation Gamma function Gauss’s summation theorem for 2F1 generalized hypergeometric function generalized hypergeometric functions tFu generalized Kummer’s summation theorem for 2F1(−1) Generalized Mittag-Leffler functions generalized Mittag-Leffler kernel (GMLK) generalized Mittag-Leffler type function h-m)-p-convex function Hermite-Hadamard inequalities Hermite–Hadamard inequality Hilfer–Hadamard fractional derivative hypergeometric function 2F1 hypergeometric functions of one and several variables inclusions initial value problems inverse subordinator Kummer’s summation theorem for 2F1(−1) Lamperti law Laplace transform Lavoie–Trottier integral formula Legendre polynomials Legendre spectral collocation method magnetic fluids magnetization Mathematics and Science Mittag-Leffler Mittag-Leffler function Mittag–Leffler functions n/a nonlocal boundary conditions Oberhettinger integral formula order statistic Pochhammer symbol Psi function Pólya-Szegö inequality random time change recurrence relations Reference, Information and Interdisciplinary subjects Research and information: general Riemann–Liouville fractional calculus operators Riemann–Liouville fractional derivative Riemann–Liouville fractional integrals separation of variables Srivastava–Daoust generalized Lauricella hypergeometric function Srivastava’s polynomials Stirling numbers of the first kind subordinator and inverse stable subordinator Wright function κ-Riemann-Liouville fractional integral
ISBN:	3036553673, 9783036553689, 3036553681, 9783036553672
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Shrnutí:	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.
ISBN:	3036553673 9783036553689 3036553681 9783036553672
DOI:	10.3390/books978-3-0365-5368-9