Fractional Calculus Operators and the Mittag-Leffler Function

• Format: eBook
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2022
• Subjects: 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
• DOI: 10.3390/books978-3-0365-5368-9

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.