Fractional Calculus Operators and the Mittag-Leffler Function

• Other Authors: Andrić, Maja (Editor)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: Research & information: general; Mathematics & science; fractional derivative; generalized Mittag-Leffler kernel (GMLK); Legendre polynomials; Legendre spectral collocation method; dynamical systems; random time change; inverse subordinator; asymptotic behavior; Mittag-Leffler function; data fitting; magnetization; magnetic fluids; Gamma function; Psi function; Pochhammer symbol; hypergeometric function 2F1; generalized hypergeometric functions tFu; Gauss'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 kind; Hilfer-Hadamard fractional derivative; Riemann-Liouville fractional derivative; Caputo fractional derivative; fractional differential equations; inclusions; nonlocal boundary conditions; existence and uniqueness; fixed point; gamma function; Beta function; Generalized Mittag-Leffler functions; generalized hypergeometric function; Fox-Wright function; recurrence relations; Riemann-Liouville fractional calculus operators; (α, h-m)-p-convex function; Fejér-Hadamard inequality; extended generalized fractional integrals; Mittag-Leffler functions; initial value problems; Laplace transform; exact solution; Chebyshev inequality; Pólya-Szegö inequality; fractional integral operators; Wright function; Srivastava's polynomials; fractional calculus operators; Lavoie-Trottier integral formula; Oberhettinger integral formula; fractional partial differential equation; boundary value problem; separation of variables; Mittag-Leffler; Abel-Gontscharoff Green's function; Hermite-Hadamard inequalities; convex function; κ-Riemann-Liouville fractional integral; Dirichlet averages; B-splines; dirichlet splines; Riemann-Liouville fractional integrals; hypergeometric functions of one and several variables; generalized Mittag-Leffler type function; Srivastava-Daoust generalized Lauricella hypergeometric function; fractional calculus; Hermite-Hadamard inequality; Fox H function; subordinator and inverse stable subordinator; Lamperti law; order statistic; n/a
• Online Access: DOAB: download the publication; DOAB: description of the publication

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.